Hot Amp!!!
I'm having trouble visualizing exactly how you have it set up. You said that the amps are "grounded through the amp" but I think you meant they're grounded through the cap. I don't think that's the cause of your problem, but the cap and amplifiers really should be grounded separately. There's no reason to run the grounds to the cap instead of directly to the chassis.
It seems more likely to me that the problem is related to your speaker wiring. I'm not clear on how your speakers are wired either; I can see that you've kept the speakers on factory wiring, and connected the amp to the factory wires. But I don't understand how that translates to having only one set of wires for both speaker sets.
We'll leave the tweeters out of it; if they're wired through a crossover, then they don't have a serious effect on the impedance. However, any way you look at it, you've got two 4-ohm speakers wired together to a bridged amplifier. Most 2-channel amps aren't designed to be connected to load impedance under 4 ohms when they're in bridged mode. If your speakers are wired in parallel, then the load impedance at the amp is 2 ohms. Having too low a load impedance is the most common cause of amplifier overheating.
My advice is to re-wire the speakers so that one 5x7 and one tweeter (together with a crossover) is connected to each amplifier channel. Don't run the amp in bridged mode.
Even in this configuration, I'd be amazed if your 5x7" speakers are really rated to handle 310 watts RMS, which is the per-channel power rating of your amp in 2-channel, 4-ohm mode. It sounds to me like you've got too big of an amp for the job.
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