This is a lot to try and cover in a forum board but lets begin.

1st, need a detailed layout of what we are working with. Specifically brand & models of 'every' piece of equipment involved (at the very least the brand):

Where is the central components located (matrix and sources)? Is it in room 1, 2, 3, or 4? Or is it located in another (5th) room?
What size matrix is it (i.e 4x4, 6x4, etc.). What sources do we have connected to it? How is the output from the matrix getting to each TV (long HDMI, cat6 over extenders, etc.)?
How is the multi-zone amp getting its audio and from where?
Are there any other sources going to the TVs, that's not coming from the matrix?
What is the longest approximate distance from the central equipment and the furthest room?

I'll start a diagram based on these answers, and prepare the next set of questions.