I ran both leads directly to the battery, and used a relay to trigger the switched lead on the Empeg so that the relay only passes the current from the battery when the key is on.

Excellent solution. Can't go wrong there and you minimise the possibility of ground loops.

when I choose a certain playlist ... it seems to lock up.

...it skips very badly...

..."invalid MP3 file"...

Hmm. very odd. Ditto as mentioned above, What player version are you using? 1.03 should not do any of this. If you unit does need repair, it will most likely be repaired not replaced.