In my early conversations with my bank, they stated that among other things, they would need to see proof of where the funds had come from (proof of original $ deposit into FTX, FTX trading history, etc.), and I just assumed that sending the crypto to a different exchange would add another layer of complexity that would make that process much harder.
But perhaps I took an overly conservative (and now catastrophic) stance when trying to do everything as cleanly as possible.
I have a sneaking feeling your approach might have worked (or at least it's hard to imagine it being a worse outcome than what actually happened). I'm feeling pretty stupid now for not exploring this further. I guess I never expected FTX would just disappear, and so I didn't explore every option as fully as I should have. I appreciate your suggestion in any case.