I appreciate your input throttlekitty, but I believe it didn't come close to what I want. However, I've actually managed to resolve the problem. Apparently all I had to do was transfer the UVs, then delete history. It does exactly what I need, where the transferred UVs turn into a new map for that object within the same UV…
Wouldn't that create additional texture sets though? I've actually managed to work around it for this specific model, but the reason why I believe overlapping would be a problem is because that means the overlapping UVs will take the material of the parent object, which is what I don't want. What I want essentially, is to…