I worked on the phone with John and Aleksandr, who were able to get the issue resolved by having me add GoDaddy to the call. Once GoDaddy was on the call, Aleksandr led them to resolving the issue, which is getting their advanced support involved to "remove the domain name from the tenant". Once this was resolved, they said it may take up to 24 hours, but I was able to immediately add the domain to the new account. For anyone else who gets this issue with a NETORG xxxxxx.onmicrosoft.com account, the end result is that GoDaddy needs to fix it from their side, even after your Office365 is complete cancelled and removed from your account. One other note, the old account would have finally expired on it's own from the Microsoft system in a month.
So again, the solution is to contact GoDaddy, have them escalate to advanced support and remove your domain from the "tenant" for your old Office365 account.
Thanks again to the support guys who helped!