Availability Group, asynchronous mode, manual/forced failover - handling identity overlap
Rather than trying to react to the failover on the new primary, I think it would make more sense to update your manual failover procedure to first change the AG to sync mode.  

Once the AG indicates that it's synchronized, then do the failover.  This way you won't have data loss.  You can then go back to async mode after the failover is completed.

See Change the Availability Mode of an Availability Replica (SQL Server) for instructions on how to make the change prior to the failover.

Note: a sync mode AG can temporarily shift into async mode if the network gets slow between the two servers


  If primary's session-timeout period is exceeded by a secondary replica, the primary replica temporarily shifts into asynchronous-commit mode for that secondary replica. When the secondary replica reconnects with the primary replica, they resume synchronous-commit mode


But according to the failover docs, a sync mode AG guarantees zero data loss during a manual failover


  This guarantees that every transaction that was committed on a former primary database has also been committed on the new primary database