The best way to synchronize old host and new host when migrating a Drupal site?
I think you're on the right track. It is nearly impossible to implement a migration project and not plan for incremental updates. The migrate module supports that with its "update" function (as shown in the screen shot). 

That said, there shouldn't be a problem of duplicate UIDs after the initial migration of data, unless you are letting people create accounts on both the legacy system and the new instance.