Thanks again for replying, @xmasbaby0! That makes sense and helps a lot!
So just to make sure I understand how it'll work, I'll wait for the IRS to refund the money (and I'll actually end up having it directly deposited into my checking account). Then, after I receive the return, I'll need to submit an amended return via snail mail and wait about 4 months for it to be processed. So am I expected to not use the funds the IRS sends for those 4 months? Considering I didn't actually retain any of the funds that triggered the 1099-R (I rolled the funds from one Roth 401(k) into another), I wouldn't expect the amended return to have an impact on my refunded dollar amount. My thoughts are to simply use the refunded dollars as if I'm not amending the return.
