I have made a mistake, and perhaps led you all astray.
It is true that in the Axopatch, the signal ground is not connected to the power ground.
But, it turns out that it's very difficult to isolate power ground from signal ground, without essentially breaking every BNC connection between the amplifier and the digitizer. And when I did that, I got a good amount of hum pickup from those now unshielded wires. At times you could find a position where the pickup was minimal, but it wasn't easy. And figure that you've got at least 3 connections at a minimum (signal output, analog input, and gain), that all equals one big pain in the butt.
This advice originated when the digitizers were the old Digidata 1200. That digitizer is specifically designed to isolate the signal ground from the power ground (most important to isolate it from the computer, whose fast switching power supply is a huge noisemaker). That all changed in the 1300 line of Digidatas.
However, it does seem that the simple act of using the grounded to non grounded plug adapter on the amplifier, does dramatically reduce the RMS noise level. Why it exactly does this, when there's still a connection between signal ground and power ground, I am not clear on.
Nevertheless, I am available to come and lay my hands on your setups, to reduce the noise. Cause it seems I'm back to that level of rationality for this whole process.
Gotta bring this up with the big guy soon.