Locked out of my DigitalOcean account – what are my options?

I have an old DigitalOcean account with an old instance running an old site I built for someone years ago. It's been happily running, so I haven't checked on it for quite a while.

The DO account was created from an email address with a domain I used for my freelance web business that has since gone defunct. I let the domain go, and it was bought by someone else.

Well, to my surprise, when I tried to log in to DO, it appears they started enforcing an MFA policy where email is the only option. Unfortunately, I cannot receive emails at that address now.

I've reached out to the new domain owner, hoping they have a catch-all address and will forward the MFA code, but no luck there yet.

DigitalOcean is taking the stance of "Sorry, nothing we can do on our end." I've asked them to escalate the issue, to mail a letter with the MFA code, to call me, anything other than email on a domain I no longer own. They're refusing to budge.

What options do I have here?

I really don't want to be forced to perform an infrastructure migration right now, but not the end of the world, I guess. I still have ssh access to my server, just not DO account access. The worrying thing is apparently I don't even have the power to shut down the account! I guess if it comes to it I just have to block the charges on my CC.