The first thing I always check for is mechanical/connection problems, as these are by far the most common issues with active basses. Is the noise from turning the EQ pots identical in every way to moving the wiring? A problem opamp with be problematic whether you move the wires or not and I think your fault lies elsewhere. My approach would be to;
1. Make sure the pots are clean - used Deoxit.
2. Ensure the battery connection is good. Snap connectors come loose or wires break internally. Battery box terminals can relax and wires break. Check the other end of the leads and make sure the preamp gets an uninterrupted supply. Make sure the switched negative lead at the instrument's socket is good and that the socket makes proper contact. Battery lead/connection issues are the #1 problem I encounter. If necessary, monitor the voltage at the circuit board while you move the connections.
3. With the cleaned pots, observe the pot terminals to make sure there's no movement when the pot is rotated. I've had instruments where the whole assembly has been loose and could shift around.
4. If moving wires causes the noise, try to isolate individual wires and use forceps/tweezers to try to determine which wire is causing a problem. Where you have a bundle, use your fingers to stabilize the rest of the wiring.
5. If possible, inspect the solder-side of the PCB under magnification. Cracked solder joints often have a circular crack around them and look gritty, but you need good light and good eyesight to see them. I use a pocket microscope or bench magnifier.
6. If the connections are via a push-on connector, unplug this and inspect the mating connections to ensure they mate properly. Use contact cleaner if necessary. Sometimes IDC ribbon connectors oxidize inside the header and need remaking or replacing.
I repair dozens of active basses each year and have not yet had to replace a board. I guess over 90% of faults are external to the preamp board.