Quote Originally Posted by Eric
I'm not sure of the pickup config for all of the basses, but I think at least one of them is noise-canceling.
The low-end Ibanzes that I've seen have been P and J, which means that the P will be hum-canceling, but the J and the P/J combo will not be. To my ear, a ground fault sounds different than single-coil hum though.

Quote Originally Posted by Eric
They have all played through the same amp to date, which I suppose could be the problem. It's an old-ish Fender amp with two inputs, a 1 x something (probably 12), and this fuzzy, cream-colored exterior instead of tolex. The amp output is then taken and put through a cheap DI box and run through the snake and into the mixer. In that way, the amp only serves as a head for the house and a monitor for the bassist. The amp is plugged into a Furman power conditioner that serves all of the PA gear on stage (e.g. digital snake, power amps for monitors, etc.).
Try unplugging the DI line from the amp and see if the noise is there through the amp alone. That way you can eliminate the amp. Then just keep working your way up through the signal chain.