I thought Uniatism were the Ukrainian Catholics living among the Russian Orthodox Catholics... Those living in the US are considered Uniate? Rome rejects the Eastern Catholics? I think you are mistaken. Rome has written encyclicals on the Eastern Churches - I'd have to look up the names of them. But Vatican 2 writes about them, considering them a bridge.
Regards
The term has a broader meaning than just "Greek Catholics" in the Ukraine. The much, and perhaps deservedly, maligned Balamand Declaration makes it clear that what you propose as a model for reunion is rejected by both particular churches.