The Beam only has an HDMI eARC connector for TV connection. 

Bluetooth is not a premium audio connection, nor is placing BEAM above the screen.

If you are absolutely committed to this scheme, I recommend installing a Bluetooth receiver and an analog to optical converter near BEAM, then use the optical to eARC converter included with BEAM.

I understand but I'm just worried about the optics stretching wires over the walls/ceiling to connect the projector to the Beam. Where should I place the Beam however? I figured centrally facing the viewer would be the place... 

Obviously, you would not want to place BEAM in mid screen. BEAM audio quality would be better if placed below the screen.

I have no experience with them, but there are WiFi methods to distribute audio. The very latest Bluetooth standards upgrade audio quality. I don’t know if your projector supports these standards. And, I don’t yet have any experience with these new standards.

With respect to wires, how would you distribute power to BEAM above the screen?

You also need to consider the possibility of lip sync issues if you’re not using HDMI. There will probably be a delay in the audio signal: unless you can delay the video too, the sound probably won’t be in sync with the picture. 

This PJ lacks even an optical output, so audio quality was clearly not a priority for Epson when designing this.