Hi R.H.Weber,
I understand that you can access to your public website with your company domain. However in the Office 365 domain page, the address of your SharePoint website is http://xxx.sharepoint.com/ and you can not change address as the process of changing domain is still ongoing.
Based on the current situation, I would like to confirm if you can login to your Public site by clicking Member Login at your website's home page? Did you receive any error messages? If so, please capture a snapshot of the error message and post here.
In addition, I would like to suggest you open your site in SharePoint designer, and then you can see the SharePoint Version. If the version is 15.X.X.X, it also might be a SharePoint Online Service Upgrade related issue. I'd like to suggest you check the Service Status in the Service Health and Planned maintenance in Office 365 admin page to see if there are any related information.
I will continue to monitor this thread for a few days and will reply to any additional posts or questions.
Thanks,
Allen Qiu