I finally got Dear ImGui working in Astralathe, which has taken far longer than it should have.
I was originally having a lot of trouble just because I wasn't sure of how to hook the right places without it being a huge pain in the ass. Some work on an unrelated project (which I might talk about later) led to me figuring out that the library I'm using, PolyHook2, actually has a bunch of useful facilities that make it a lot easier than I originally thought.
So, armed with new knowledge, we finally have Dear ImGui working in Psychonauts. I'm hoping that this will lead to Astralathe being a lot more user-friendly because I can now hopefully add in-game menus to configure various things. This console is all there is right now, though.