Interference does an awful lot. The "DC" created by the alternator is extremely dirty and I'll put beer, right now, on you getting an engine rev-related whine that requires the tablet to be on battery before it goes away. Cigarette lighter USB power adapters don't help because they tend to be cheap and cheerful and the varying "ground" voltages cause massive interference. I've tried running laptops in the car before and had nothing but trouble. It's extremely common. Ways round it generally include shielding RCA cables correctly (that would be with the shield connected only at the source end), mutual ground points, and a good connection back to ground. You're also running your source directly above some 90's electronics, otherwise known as the climate control.
I've had enough problems with PAs in the office, so much so that we'll now only ever run from one socket for source and active speakers, or we end up with 50Hz hum everywhere.
It's also not the 12V that will blow things up, it's the direct short between 12V and ground (chassis) with fat cables.
75W x 4 is still actually quite a bit, current wise. Even at 90% efficiency, that's a good 30A at full power. I'd probably fuse at 30A or so and use 6mm2 for the amp on both sides. Remember you're fusing to protect the cable from too much current, not the amp.
- Bret