I printed out my emergency removal password three times, and put each in a safe place. I did this because I know what I'll have to deal with if my phone dies, and I don't have the password.

If you don't have that password, you are going to have to prove your identity to SE before they will remove the OTP. That will probably require emailing or faxing a copy of your photo ID at the very least. The really bad part about this process is, as Ricje stated, their support department is still swamped. I closed two tickets yesterday, that I had open for over a week each. One of them (for FFXI) resolved itself, the other was a minor issue. I closed them to do what little I could do to lessen the strain on SE support.

Good luck to you, I sincerely hope you are able to get this resolved as expeditiously as possible