If the amp is quiet with nothing plugged into the input, this means that the interference signal is entering from the bass or wiring.
Now, when it's quiet using humbuckers but noisy using single coil (or split coil), this confirms that the noise is environmental and is entering the bass through the pickups. In humbucking mode, this cancels common mode environmental noise, which is working as it should. The same thing applies to the Nordstrand pickups, which allow you to sweep between single coil and hum bucking, and the noise nulls out when fully humbucking. Also, the noise profile is mostly 50 (or 60Hz) with very little second or third harmonics which also indicates that the noise is radiated from the power source and is unrelated to the amp's power supply. I bet the noise changes with your position in the room, or just turning it around a bit?
Things that cause this include an amp with a noisy line frequency (lead sled) transformer that has a loose radiated electro-magentic field, large motors, some lighting, and some old school fans. There is a slight possibility that the noise is due to circulating currents in your power ground/earthing system, but unlikely since the amp would usually have some noise with nothing plugged into it.