An update on this: The process seems automated and the account was unlocked 2 weeks after unlinking. The e-mail was sent exactly 24 hours before the unlinking to give me the best chance of resecuring my account before someone else got in. However, this fiasco is still not over...
After getting access to my account, I promptly went in there and locked myself out again. /sigh.
Apparently there is a bug and I am speculating as to what it is. I am guessing that the unlinking code does not delete the old 2FA and it's kept around and bound to another UI element. I suspect this because if you select "software authenticator" as what you want to relink with (It's usually not a selectable option, you have to pick an actual OTP), none of the OTPs which I created worked. Should have pulled up
https://bitcointalk.org/index.php?topic=111943.0 and stepped through it instead of assuming I could fill out the page by myself. What a nightmare. If they don't fix this for me I'll be locked out for a month.