That's almost an entire work day wasted.
When we were on Go Daddy years ago, we had a similar limit of only one domain per account for the plan we were on. But using domain forwarding (or whatever they called it) plus mod_rewrite we were able to get around that limitation and host multiple domains on the account.
I think it was called domain forwarding where you can point another domain name at your hosting account. Under normal circumstances, the secondary domain would display your main site, since all you could have is one domain name. Using mod_rewrite, we caught the request for the forwarded domain and rewrote the request to a subfolder which held the secondary website. So instead of displaying the main site, the forwarded domain would display the intended second site.
In that way we got around Go Daddy's one hosted domain per account limit.
I don't know if that will work with your web host. You can try it and see.
It was called domain aliasing when we were on Go Daddy. I found the old thread where I asked how it could be done and where dklynn gave me great advice.