I'm sorry. The products are what they are, and the Z series is just not meant to be used like that. It's important to think about a design before buying the hardware.
In your case the valid design would probably have been:
-An MX or a Z (after taking a good look at the differences between the two) in the first room
-Connected to that an AP for the room it's in
-And then a cable running to the second room
-There another access point would be connected to the cable with optionally - depending on the need for a wired connection - a switch in between.
Powering the APs either over PoE if the MX/Z and optional switch were chosen with PoE support or PoE injectors (which in smaller deployments like this may be more economical).