You need a nap, a nap and a cheap IR repeater. It ain't rocket science, as they say around here. If the remote is IR, the put a receiver in your big room, and the transmitting in line of sight of the dust collector, and open a beer. I have used a Recon (I think?) and a Terk Leapfrog. The Leapfrog cost about $50 but works much better than the $20 Recon. But, if you only need on/off, I would try the cheap one from somewhere with a good return policy. My problem was it was not overly accurate - channel 753 was 73, then 53, then 3, then I threw the remote, yatta, yatta, yatta.
In fact, I still have them and don't use them. I'm keeping the Frog for use to control the outdoor speakers (since my RF connection is broken to zone 2 now that I have a HT!). But if I can find the various plugs and eyes, I'll send you the old one. If it works, great, if not, trash it. PM me if you are interested. For the price you might prefer not to wait for met to find it! That layered thing can be tricky.
Also, look at Smarthouse (or smarthome?) .com. They have tons of options for IR repeating if you want to go upscale with it - nice wall plates, etc.
Panny 3000 PJ, 118" Carada, Denon 3300, PS3, Axiom QS8, PSB 5T, B&W sub, levitating speaker wire