I don’t have any recommendations for that budget, if you want to preserve the audio quality as much as possible.
There are options that I could recommend without changing your current equipment but not cheap, such as "good quality" audio transmitters that will send the audio signal from your receiver’s individual outputs to receivers located to the rear and then via wire to separate audio amplifiers and to the speakers, or directly to self-powered speakers, eliminating wires running from front to rear. Similar to what is used in concerts. The problem with this option is that it MAY suffer from undesirable latency, for which additional processing may be needed.
I would spend a few hundred dollars on good quality/gauge speakers wires and go up the wall into the attic and drop the wires back down the wall/s near to your speakers.
I did that, although it involved the dreaded attic insulation and a few hours of my time.
You didn’t mention if you have hard floors, carpet, a rug or a basement. There are flat speaker wires and cables that are practically undetectable by walking over them and you can run them under a rug or carpet.
Maybe a nice rug is the answer and may improve your room’s acoustics all at once!