Any other options besides Xirium? I only need one channel.
How much range do you need.
I know Sennheiser in ear transmitters with work with their wireless mic receivers as an audio RF link.
How is the remote amp and equipment going to be powered on and off. Is the circuit that it will power it on a separate breaker that they will try to remember to turn off when the games are over. You could use an audio sensing relay (RDL makes one) and have it close an AC power relay to turn on the amp, the receiver would have to be on the whole time though or move the AC auto powering set up back to the main building...if that's the building feeding the power to the remote amp.
For just about any amp stuck in a box it will need some form of venting.
Here's another idea, Technomad already has weather proofed amps and it looks like they have a wireless audio link option as well. It actually looks like there using a modded Hammond style cabinet.
https://www.technomad.com/products/powerchiton/