Right,
I am no specialist, but three solutions that I can think of are:
– not Baking…(apart from the 10000’s of experience points you gained, is there really an advantage? It’s not a game-ready model anyway…)
– your suggested solution of moving parts to another UDIM Tile..(a lot of work, but best result if Baking is necessary…)
– leaving it as it is now. As Omar said, it is looking amazing already, even with the Baked Textures.