Run a battery isolator if you plan to add extra batteries in your vehicle.
I would think that you amp cutting out is a capacitance problem not a grounding problem.
Running cable from the front of your vehicle to the back is fine for the 12v+ but the entire body and chassis is a ground.
A long ground wire directly to the battery might get you slightly better power (SLIGHTLY) but it will very likely cause inducted noise. 95% of inducted noise is usually from improper/poor grounding in a DC electrical system.
Burp trucks and SPL guys don't give a rats ass about engine whine, alternator hum, or ground loop noise. They are not listening to the system for audio quality, they are looking for max output.
They can run multiple long run ground cables if they want (again only a minor improvement electrically) because they don't care if it creates a small amount of whine or hum.
As previously prescribed: definitely do a big 3 upgrade and also consider adding a capacitor.