Hope you are well and sorry to hear you are having these issues. You are correct in what you were advised, the mailboxes do need to be deactivated in order for you to migrate the domain to the new O365 tenant. If you are getting errors on the website this may need to be escalated to our second line team to resolve for you, as it is likely just an issue with our systems rather than anything on your end.
You could ring 0800 800 154 and speak to a member of our technical helpdesk - they will be able to take a look and escalate if need be, but I think you may be better contacting our DNS team. They are also on livechat but they should have access to the systems needed to get this sorted. You can speak to them directly at dnsforms.co.uk. There are also little forms there you can fill out for several issues, and I believe that domain transfer is one of them, so if you do not have time to livechat you can fill that out and someone should contact you back. 🙂
I hoep you can get this all sorted without any further issue!