Hmmm. You know, I think it is overkill to provide two separate isolated supplies for these two. My gut says that this should work fine on one supply, and the fact that it doesn't has something to do with the audio interface between the two, not with ground loops. Ground loops are typically a problem when you share grounds and/or when you have very sensitive interfaces followed by a lot of gain.
If you connect each device to the battery ground directly with its own wire, and you use the lead-acid battery (which is very low impedance) then there is no shared ground currents on the power supply negative wires. The problem may be in the two connections that join audio from one box to the other. It could be that one is balanced while the other is not. I suspect something like this, or perhaps there is a DC bias on one line that the other cannot tolerate. A simple experiment is to make the audio connection using a large value non-polarized cap on the Audio+ and the same thing on Audio-. You can form such a capacitor by joining two large electrolytics + to + and then use the remaining two leads as one capacitor.