How about some
CDT-61a Component Speakers driven by a
US Acoustics USX-4085 with the amp's rear channels bridged to a
Blueprint BPD-1202 Subwoofer (build your own box). Be sure to grab a
KnuKonceptz 4ch 4ga Amplifier Wiring Kit. Components - $150
Amp - $175
Subwoofer - $97
Amp wiring kit - $36
Box building supplies - around $30
Total w/o shipping = $488
FWIW, RF hasn't made stuff with a good performance/$ ratio since back in the day. Also, you'd be better off disconnecting your rear speakers after installing a system like the one I described.
P.S. I still don't think your factory amp is properly bypassed. The symptoms you're describing are exactly what happens when running speaker outputs from an aftermarket HU into the factory amp. I'd suggest finding a new 'stereo guy'.