The key was to deal with the wall-wart appropriately. I used to poo-poo them until I realized that if used in the right fashion they could be fine. And you have to use the right kind of wall-wart. It has to be unregulated, just a transformer, diodes, and caps. Beyond that I did some fancy filtering at the PICCOLO dc input to remove any additional noise. As a result, I was able to remove all traces of ac induced hum from the PICCOLO.
The question is are the internal batteries any better? Well, maybe, but only in the sense that there are now fewer external cables to route (and the potential for coupling). One less gadget sucking power from the wall. So, theoretically yes. But I have not been able to hear it sonically. Maybe someone else here has.
jh