It is very difficult to comment on something with no knowledge about the system, business requirements etc. Moving a customer from one tenant to another, sounds suspect to me, but I don't know what "tenant" means here.
Generally, when you decide to for partitioning, you need to consider does the partition key appear in all queries? If you have queries there WHERE or join condition does include the partitioning key, you can expect these queries to take a hit.
As for the migration path you outline, it is again difficult to evaluate without further knowledge of the system. But keep in mind that if the system while you are running migration to the new database(s), you will need to deal with data changes that occurring the migration process. This requires careful consideration, and not the least careful testing.