:("Due to system issue, our backend team was unable to migrate the Mobile Services from source to destination subscription and they are working to fix it but we do not have any ETA for it.You would need to back up the Mobile Services from Source subscription and re-deploy it to the destination subscription. I sincerely apologies for any inconvenience caused due to this."
Yep, I need to delete the existing services and then recreate them on the other subscription. Even though they previously, after 2 weeks back and forth, was told they could do it. And all this time I'm paying for something that would be free on the other subscription.
Okay, it's a good test of my backups and ability to recreate these services if something went wrong but I can't help feel that I'm working round what should really just be a setting on their end. After all, it is a setting for some of the other services.
The lesson in all this: Moving services between subscriptions is a lot harder than it should be. If you have to do this in the future, be aware of possibly having to delete and recreate services yourself. In fact it will probably be quicker (and cheaper?) if you just do this yourself and don't ask them to do it for you.
Lesson 2: This was handled by the billing support department of Azure. This is the free support that everyone gets. This is not from the, paid, technical support. - I guess I'm gettting what I'm paying for.