You're ****ed!
Sorry dude just had too. The reason it might be cutting out at high volume is cause it draining to much power and the alternator can't keep up with it.
Engine noise, means your RCA wires too are close to some power wire(s). Or your Radios a POS. If you ran the RCA away from all power wire, then you need to ground the RCA wire better. Take a little wire and slip it under the lip of the rca, ground the wire to the radio.
Sometimes running the power wire next to something that puts out high voltage can create noise. Like having the wire ran next to the coil. I'm afriad to ask the details on your wiring. I use to do custom audio..........most of the time I had to re-wire whole systems. I first started by ripping everything out literally and starting over. good luck.
Also how far is your ground from your radio?