I am all for the different masks, but that when a person makes many people out of himself. Here we have Tom Riddle who is definitely was born and David Monroe who was born(*), and Q.Q. who was born, and Harry’s teacher could be only one of those three (or someone else entirely), but not the three at once.
(*)I mean a boy, a baby, not the “returned from Albania” one.
Dumbledore gets the map from the twins, doesn’t give it back and the twins don’t remember about it anymore. So, we know who’d obliviated the twins. However, we don’t know the results of D’s “find Tom Riddle” order… Also, the twins must’ve known about Harry’s time travels by way of the map?