The ultimate solution to ground current problems is to eliminate the ground current from the signal lines. That means a transformer, an optical link, or the traditional balanced line. Naturally all of these are compromises, one way or another. Pick your poison!
Non-ultimate solutions involve reducing the resistance of the signal-ground line in which the current is flowing, or reducing the current itself. Naturally, "reducing the current" means sleuthing out the source(s) of that current - never an easy task, but sometimes an interesting challenge!