Just my own opinion here, my own experiences with single wire altenators was not very good. I would suggest that you go back to the std wireing for the alternator. It's only 2 or 3 more wires, much more accurate vootage control and quicker pick up than the single wire.
i do suggest that you check all grounds. Especially check for proper grounding of the alternator itself. It grounds through the case to the bracket, then on to the engine/engine ground. May need to run a direct ground from the alternator itself to the frame. I wouldn't think that a bad battery would do it, but this whole situation is odd, so anything is possible.
