It could be that an older version of CbB and BA would work. but that assumes you have access to to them.
Maybe it's best to wait for the next update, or an even later update, and hope that works.
If it were a desktop, I would try cloning the drive on your windows 8.1 computer and putting it in the new one. but that is not possible with a laptop, of course. And Microsoft might not let you do that anyway. Probably would run into authorizing issues. They frequently will let you do things like that if you call them and explain the situation. At least they used to. These days who knows.
Is your copy of Windows 8.1 retail or OEM? If retail, you can install it on the laptop and it should authorize. That may solve the problem. Plus, you won't have to fight Windows 10 trying to spy on you, force updates etc.
I would keep trying, and keep doing what the knowledgeable folks here are suggesting. At some point it will probably click. If not, use that laptop for linux and get yourself another one and hope for better luck.