This is very elaborate! Don’t think I’d ever have the patience to go through the steps.
However, it reminded me of trying to visualize mathematical objects. Somehow these are more concrete than what you are describing though. For example, when learning linear algebra, I (and probably many others) would visualize various bases, subspaces etc. as arrows or planes in space, often in more than 3 dimensions. When I was learning General Relativity, I needed to imagine tensors. A symmetric tensor is sort of like a fuzzy squished egg, stretching and squeezing whatever it engulfs without changing its volume, but also separately compressing or blowing up the whole thing overall. An antisymmetric tensor is like a multi-dimensional hurricane, spinning whatever it comes across in various directions, in addition to overall stretching/squeezing. Once you develop the relevant intuition, the answer to a specific problem in the domain often comes to you long before you can figure out how to get it. John Wheeler, the guy who gave black holes their name, was famous for that. Anecdotally, a lot of mathematicians are like that.
On the other hand, maybe mathematical objects do not count as abstract objects anymore, if they are the object of your study. On the third hand, category theory is as abstract as it gets, and those fluent in it do “diagram chasing” mentally all the time. Still, maybe it’s not what you are talking about at all.
This is very elaborate! Don’t think I’d ever have the patience to go through the steps.
However, it reminded me of trying to visualize mathematical objects. Somehow these are more concrete than what you are describing though. For example, when learning linear algebra, I (and probably many others) would visualize various bases, subspaces etc. as arrows or planes in space, often in more than 3 dimensions. When I was learning General Relativity, I needed to imagine tensors. A symmetric tensor is sort of like a fuzzy squished egg, stretching and squeezing whatever it engulfs without changing its volume, but also separately compressing or blowing up the whole thing overall. An antisymmetric tensor is like a multi-dimensional hurricane, spinning whatever it comes across in various directions, in addition to overall stretching/squeezing. Once you develop the relevant intuition, the answer to a specific problem in the domain often comes to you long before you can figure out how to get it. John Wheeler, the guy who gave black holes their name, was famous for that. Anecdotally, a lot of mathematicians are like that.
On the other hand, maybe mathematical objects do not count as abstract objects anymore, if they are the object of your study. On the third hand, category theory is as abstract as it gets, and those fluent in it do “diagram chasing” mentally all the time. Still, maybe it’s not what you are talking about at all.