Even having a Global Resync button that we could occasionally press in a view that would then resync those threads would help relieve some of the annoyance.

Or a rule that checks the recent notes that were made on a ticket/thread and forces a resync IF the note starts or contains: "This ticket was completed and merged into" Since the Inbox is able to show the updated note that it's been merged, just didn't receive the webhook from Autotask to run another item on thread.