Maybe you can take an idea I had and make it work for you
In the living room at what's her face's place is rolled out a very nice Pakistani rug. Like you, she has a situation where she has a 5.1 system set up but there is no path to the rear of the room that doesn't cross an opening, so the only options are either run wires in wall, through attic (which would involve pulling up floor) and back down wall (which would be difficult as that wall actually is mostly picture window) a non starter for several reasons.
So I initially set up her system with one of those molded rubber things that are used in conference rooms to keep people from tripping on network wires, extension cords, etc. and ran the two rear channels and sub RCA cable in it. It's still like that but my THOUGHT was...
the rug has probably a 1/4" thick pad underneath it. My thought was to cut a channel in the bottom of the pad, and use that to run the wires. I haven't quite figured out the logistics of the idea however, and also if I screwed it up I'd have to buy another $100ish pad...