To move an Azure subscription to a new tenant, you'd normally follow the process that you've described.
This sometimes doesn't work if the subscription SKU isn't supported in the enrolment you're moving to.
I'd try one of these two things
- Raise an Azure support request to check if they're able to move the subscription to a new tenant for you
- Add a guest account from the other tenant to your subscriptions AAD. The use Azure Resource Mover on the individual resource groups to an existing subscription in the right tenant.