For anyone else dealing with this issue, support responded to my ticket with confirmation that it is a billing issue (! - How is this taking so long?) and a workaround that doesn't really solve my problem, but may help some:
I had a look at the account and this issue is occurring because, we’re currently updating our internal billing system, and this process is preventing some domains from moving between sites. I’ve escalated your case to our engineers, and this issue will be resolved as soon as possible.
ince your custom domain can’t be moved at this time, you can forward it to your new site’s built-in domain as a temporary workaround. With this workaround in place, your site’s built-in domain will display publicly.
To forward the original domain to your new site’s built-in or custom domain, log into your old site and follow the steps in this guide:
While the steps in the guide above appear to be for forwarding a domain to a non-Squarespace site, they can also be used to forward to another Squarespace site. When forwarding the original domain, enter the new site’s built-in domain or the custom domain you purchased into the URL field. If you need help finding your site’s built-in domain, visit this guide: