Well, as for the dementor manipulation ability as the “power the Dark Lord knows not”, it is actually a pretty overpowered one. Considering that in HPMOR universe dementors are described as Death, “wounds in the world” and whatever else, they should make a very effective weapon. Consider that, for example, when Harry asks about what would happen if a dementor got thrown into the sun, people seem to interpret it not as a “would a dementor die?” sort of question, but as a “would the sun get damaged by that?” question. So, in my opinion, such a monster shouldn’t be inhibited by such things as mere large distances, material obstacles and other mundane and magical protections. When Harry stood before the Wizengamot in a presence of some pretty powerful wizards, including Dumbledore, McGonnagal and Lucius, he was quite sure that in the absence of Patronuses a single dementor under his control would be sufficient to quickly and selectively wipe out everyone who Harry found distasteful. Note also, that there is no need for Harry to wave his wand or say anything to control dementors.
So, if Harry could get his hands on a dementor and his moral qualms wouldn’t get in the way, I am sure that at the very least he could kill every death eater he wants dead (maybe sparing Lucius and Sirius, former as a possible ally, latter for a bit of questioning), and discorporate Voldemort, which would at least give him time to call for backup and warn people while Voldie is busy respawning and looking for some Listerine to wash that truly horrible dementor aftertaste out of his mouth. As for Voldemort’s idea that he could run away from his body before it gets kissed—I think Voldie is overestimating himself here. Dementors are controlled by people’s (especially Harry’s) expectations, so if Harry expects a dementor to insta-kiss Voldemort, then Voldemort should be toast.
There are a few of ways to take this idea further than Harry’s immediate survival. First, we don’t know yet how a dementor’s soul-munching abilities interact with a horcruxed spirit, so it is possible that a Kissed Voldemort would die completely or come back damaged. Second, even if Voldie can come back from being kissed, Harry could do the following—tell Voldemort (maybe in the course of explaining the dementor-control power) in Parseltongue that the dementors are going to purposefully hunt down his horcruxes (being entropy personified, they might be able to slowly erode them and wouldn’t be held back by such mundane inconveniences as said horcruxes being in Earth’s mantle or something) and kiss any body that Voldemort enters. This sets the new expectations in Voldemort’s mind (even if he finds it laughable) and then Harry unleashes the Death.
Now, the question is: where does Harry get a dementor? I guess Harry might have a sudden realization that being Death, dementors should not be bound by such trivialities as a mere few hundred kilometers, and summon some from Azkaban, but EY might consider that a revelation that bypasses the previously set constraints. Alternatively, Harry might try to gamble by telling Voldie that he knows a counterspell to dismiss Death (which does sound useful to an aspiring immortal), and hope that Voldemort doesn’t realize the dementor connection and is actually willing to try an experiment with the sword and rope ritual. (and hope that the ritual actually produces a dementor and not some other variation of Death Incarnate).
Actually, now that I spent a little time thinking on it, this idea becomes even more interesting. Remember, one of the recurring themes that makes Harry so cool is that he has different conceptual limitations from the rest of the wizards. Now, as far as we know, dementors are controlled by people’s expectations. The reason that dementors haven’t exterminated all the life on Earth yet could be that while people are afraid of death, death always seems to wait another day and moves slowly and on its own pace. I mean, for a medieval person, the image of death might be connected to a tiger or a warrior on horseback killing you or disease or hunger doing you in over the course of several days or maybe weeks. Barring freak accidents, the fastest death-related image in a medieval person’s brain could be an arrow (or a fast-flying but perfectly dodgeable Avada Kedavra bolt for a wizard).
So, the Wizengamot people whom Harry considered unleashing a dementor upon, and the Death Eaters surrounding him now—they are all medievals. Voldemort, at least, has contemplated nuclear missiles, rockets and spaceships, so for him death could imaginably be something that can cover a good portion of Earth’s circumference in under half an hour, reenter the atmosphere at many times the speed of sound and blow a whole city to the oblivion. Voldemort, however, haven’t internalized as much physics as Harry did, so he is on the level of a mid-20th century science fiction writer—and he doesn’t have the power to control dementors.
Harry, however, is a totally different case. Harry can imagine (and, quite possible, given time and money, construct) a laser cannon that shoots a ray of death at the speed of light. Harry can think of supernova blasts covering interstellar distances. Harry can think of ultra-relativistic projectiles carrying enough kinetic energy to completely blow a planet apart. Harry can think in terms of homing missiles and AI-directed weapons that can track and destroy enemies without a need for human guidance. Hell, now that Harry knows that time-travel is possible in this universe, he should be able to realize that this could lead to FTL signaling (which could be used to kill people faster than light), so in his mind, death literally shouldn’t have a physically set speed-limit. And with his Partial Transfiguration, Harry already has demonstrated his capablility of using his knowledge to bypass the concepts that hold the rest of the wizards back. And Harry does have the power to control dementors.
So, to summarize the above—Harry is the only person who can truly control dementors, and in his mind, Death has no speed limit. If Harry can figure this out within the remaining 60 seconds—Voldie and Death Eaters simply don’t have any chance.
Well, as for the dementor manipulation ability as the “power the Dark Lord knows not”, it is actually a pretty overpowered one. Considering that in HPMOR universe dementors are described as Death, “wounds in the world” and whatever else, they should make a very effective weapon. Consider that, for example, when Harry asks about what would happen if a dementor got thrown into the sun, people seem to interpret it not as a “would a dementor die?” sort of question, but as a “would the sun get damaged by that?” question. So, in my opinion, such a monster shouldn’t be inhibited by such things as mere large distances, material obstacles and other mundane and magical protections. When Harry stood before the Wizengamot in a presence of some pretty powerful wizards, including Dumbledore, McGonnagal and Lucius, he was quite sure that in the absence of Patronuses a single dementor under his control would be sufficient to quickly and selectively wipe out everyone who Harry found distasteful. Note also, that there is no need for Harry to wave his wand or say anything to control dementors.
So, if Harry could get his hands on a dementor and his moral qualms wouldn’t get in the way, I am sure that at the very least he could kill every death eater he wants dead (maybe sparing Lucius and Sirius, former as a possible ally, latter for a bit of questioning), and discorporate Voldemort, which would at least give him time to call for backup and warn people while Voldie is busy respawning and looking for some Listerine to wash that truly horrible dementor aftertaste out of his mouth. As for Voldemort’s idea that he could run away from his body before it gets kissed—I think Voldie is overestimating himself here. Dementors are controlled by people’s (especially Harry’s) expectations, so if Harry expects a dementor to insta-kiss Voldemort, then Voldemort should be toast.
There are a few of ways to take this idea further than Harry’s immediate survival. First, we don’t know yet how a dementor’s soul-munching abilities interact with a horcruxed spirit, so it is possible that a Kissed Voldemort would die completely or come back damaged.
Second, even if Voldie can come back from being kissed, Harry could do the following—tell Voldemort (maybe in the course of explaining the dementor-control power) in Parseltongue that the dementors are going to purposefully hunt down his horcruxes (being entropy personified, they might be able to slowly erode them and wouldn’t be held back by such mundane inconveniences as said horcruxes being in Earth’s mantle or something) and kiss any body that Voldemort enters. This sets the new expectations in Voldemort’s mind (even if he finds it laughable) and then Harry unleashes the Death.
Now, the question is: where does Harry get a dementor? I guess Harry might have a sudden realization that being Death, dementors should not be bound by such trivialities as a mere few hundred kilometers, and summon some from Azkaban, but EY might consider that a revelation that bypasses the previously set constraints. Alternatively, Harry might try to gamble by telling Voldie that he knows a counterspell to dismiss Death (which does sound useful to an aspiring immortal), and hope that Voldemort doesn’t realize the dementor connection and is actually willing to try an experiment with the sword and rope ritual. (and hope that the ritual actually produces a dementor and not some other variation of Death Incarnate).
Actually, now that I spent a little time thinking on it, this idea becomes even more interesting. Remember, one of the recurring themes that makes Harry so cool is that he has different conceptual limitations from the rest of the wizards. Now, as far as we know, dementors are controlled by people’s expectations. The reason that dementors haven’t exterminated all the life on Earth yet could be that while people are afraid of death, death always seems to wait another day and moves slowly and on its own pace. I mean, for a medieval person, the image of death might be connected to a tiger or a warrior on horseback killing you or disease or hunger doing you in over the course of several days or maybe weeks. Barring freak accidents, the fastest death-related image in a medieval person’s brain could be an arrow (or a fast-flying but perfectly dodgeable Avada Kedavra bolt for a wizard).
So, the Wizengamot people whom Harry considered unleashing a dementor upon, and the Death Eaters surrounding him now—they are all medievals. Voldemort, at least, has contemplated nuclear missiles, rockets and spaceships, so for him death could imaginably be something that can cover a good portion of Earth’s circumference in under half an hour, reenter the atmosphere at many times the speed of sound and blow a whole city to the oblivion. Voldemort, however, haven’t internalized as much physics as Harry did, so he is on the level of a mid-20th century science fiction writer—and he doesn’t have the power to control dementors.
Harry, however, is a totally different case. Harry can imagine (and, quite possible, given time and money, construct) a laser cannon that shoots a ray of death at the speed of light. Harry can think of supernova blasts covering interstellar distances. Harry can think of ultra-relativistic projectiles carrying enough kinetic energy to completely blow a planet apart. Harry can think in terms of homing missiles and AI-directed weapons that can track and destroy enemies without a need for human guidance. Hell, now that Harry knows that time-travel is possible in this universe, he should be able to realize that this could lead to FTL signaling (which could be used to kill people faster than light), so in his mind, death literally shouldn’t have a physically set speed-limit. And with his Partial Transfiguration, Harry already has demonstrated his capablility of using his knowledge to bypass the concepts that hold the rest of the wizards back. And Harry does have the power to control dementors.
So, to summarize the above—Harry is the only person who can truly control dementors, and in his mind, Death has no speed limit. If Harry can figure this out within the remaining 60 seconds—Voldie and Death Eaters simply don’t have any chance.