I had a similar problem, where running the fronts and rears to the same amplifier caused a ground loop, but running them to two different amplifiers did not cause a ground loop.

Very interesting!

Are you using the exact same type/length of cable for both runs? If not, try doing that and see if it solves the problem.

Another thing to try. If the amp has pass-through connectors, try passing the rears from the fronts at the amp, with only one pair from the player. You will lose the ability to fade from the head unit, but you will get all four speakers working and then you can adjust the fade by fiddling with the amp gains. If you don't have pass-throughs, try Y-adapters. These various options are illustrated here.

Of course, make sure to go through the ground-loop troubleshooting documents linked in the FAQ.