There are two potential synchronization considerations in this system.

First, is the obvious lip sync between PLAYBAR audio output and the TV picture. Some lip sync issues are built into the source. It is not likely that the matrix or balun will exacerbate source lip sync issues.

Second, is audio synchronization between the house and PLAYBAR. As you calculate your delays, add 35ms for PLAYBAR -- plus whatever is added by the TV's own processing.

Edit: spelling