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I decided to put it on hold and come back to it.  But...platforms merging together was happening well before that glitch.  It might have been a thing that mostly happened offscreen--like, when I moved a platform in a way that made it intersect something on the next screen, the two ended up joined.

Yup, that seems to happen exactly like you say when you move something to a room you haven't visited yet (the room isn't activated yet so the objects within it have no collisions). And then when you try to move one of the "joined" pieces, it might just jitter like you mentioned.