Tom,
You are correct, if the wave shape is set to square the signal should be completely off on part of the wave cycle. But since this is a harmonic tremolo, you need to make sure the mix knob is exactly at 12:00 so both sides (hi and low) are working equally. Keep the depth knob at max when testing this. Also, in testing this, make sure the phase switch is set to “in” so both sides are working together, otherwise one side will be on while the other is off, making it hard to tell if either side is completely turning off.
The best test you can do to ensure the pedal is working correctly in this way is to put the pedal in calibration mode to test each side individually to ensure it is fully turning off.
This is most likely an issue with the analog side of the circuit, so re-flashing the pedal won’t help.
The volume knob issue sounds like a bad solder joint somewhere in the signal path. Consider re-flowing all the joints in the signal path. Make sure to use enough solder on each joint and make sure you are using enough heat to get the solder to flow properly.
Let me know what you find after you test it in calibration mode.
-Brach