This may be a pain to do, but could you get a picture of the back side of the amp that's under the radio? It should have 3 connectors going into it, one from the radio, one out to the front speakers, and a separate harness out to the rear speakers. The symptoms you have are what you get when you have a non-mach amp in the dash in place of the mach460 amp. The correct one has a crossover built in that routes the base to the rear amps. It's either that, or the guy has cut/spliced the wiring for the woofers to use another amp in the trunk (in your picture of the cut wires, is that red wire a large gauge wire for an amp hanging out from where the rear seat mounts? If it is I'd say you need to check the wiring in that harness you have a picture of to make sure he didn't cut the existing wires from the amps, and splice in for an external amp. He could have done that, and used the existing woofer wiring in the car to get signal to the existing speakers (that's what I ended up doing when I gutted the mach460 stuff out of mine, used the tweater wiring in the front to go to a clarion xc1410 in the dash, wired to kicker seperates in the doors and rear boxes in my vert, just need to add a sub in the trunk and I'm done with my stereo upgrades, sounds 1000x better than the mach system did on my aftermarket radio).
Your best bet at this point would be to make certain that you have no cuts/splices in the existing wiring. Measure the ohms on the speaker outputs on the existing rear mach amps (the 2 wire connector on each amp), I'm thinking that it reads 2 ohm, since it's wired in parallel with 2 4ohm speakers... Also remember that the amps in the back are NOT stereo, they are single mono amps, with the left side woofers (front and back) wired in parallel on one side, right side woofers on the other. Also remember that the amp turn on circuit required for the mach 460 amps requires a much lower voltage than your aftermarket radio will put out (I think around 6v is what they want to be happy), so you'll need a set of resistors wired inline with the amp turn on circuit otherwise it'll make an annoying thump/pop on turn on.
Also not sure if it's been posted here in thread or not, but lots of good info on the mach systems over at the flemworld site:
http://www.flemworld.com/mach460/mach.html