to clarify on the 2nd portion - when you moved the rear speaker forward, it began to static, but did the (former) front speaker produce static when connected to the rear? If the speaker changes but static is produced only on one channel (ie only when connected to the wires in the front door) then the channel is the problem, so either wires or amp. If the static moves with the speaker, the speaker is the problem.
Speakers 'buzzing' and cutting out is usually a wiring problem, so check for good soldered or crimped (or even well twisted/taped) connections to the speakers, good connection at the amp, and at the head unit.
Since you can physically move the speaker to cause symptoms, I would say it is almost certainly a wiring problem.
No longer own: '12 V6 Perf, from Sept '11.
Mods: TWM 520g Piston shift knob & Barton shift bracket, AM short shifter. SR 1.5"drop & AM street phb. Tokico D-spec, Whiteline bars F&R, J&M Lca, 25mm wheel spacers, 18x10x4 Bullit style on Sumimoto rubber. Magnaflow Street's. 25' of b-quiet ultimate, 10" JL [email protected] 350w, JL TR's upfront. Bama Tune, B&M 73mm & Shorty headers.
Someday..... Twin Turbo, or SC goal is 450 whp. Has to wait until warranty is up