Aso-san showed me how to properly replace the potentiometers in the servo boards. So I hoped it was just the knob that was broken and not the variable resistor itself.
I took a replacement control knob from the elec shop, there's a lot of them.
Before reattaching I rotated the knob to about 5 out of 10, since the threshold was previously stuck at 0 volts, which is the middle of the range setting.
Unfortunately, the threshold out reading is still broken, as is the SHG lock. Threshold out reads zero normally, but when the dial is rotated there is a threshold voltage reading the magnitude of which depends on the rotation speed. So I think the potentiometer and threshold power supply connection work and there is a small circuit break somewhere common to the error signal and Threshold out reading, which is small enough such that the capacitance can detect a fast change in the potentiometer voltage divider.
I suspect the circuit break is at the marked location since neither the THRESHOLD OUT nor the SHG lock work correctly when the threshold dial is adjusted over the full range. However, THRESHOLD OUT can detect fast changes in the value, so the power supply connection and potentiometer probably still work.
Unfortunately the suspect point is the connection to screw terminal J14 and resistor R104 which is in a very inconvenient location.
SHG threshold and Auto Lock magically fixed itself and I don't know how or why. It even returned to the same value I had set (9 V). Output green is 310-320 mW, same as before.