To address your question of how to do backdoor, I don't see why you couldn't convert from the Traditional IRA you use for the rechacterization. Or if you just withdraw the excess funds make a new contribution (within the correct time for such contributions). But I could be missing something.
https://www.irs.gov/retirement-plans/retirement-plans-faqs-regarding-iras
what you cannot do is recharacterize a Roth conversion to a traditional IRA.
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