The preset resistor in question is part of the Astable 555 oscillator circuit necessary for generating a continuous train of square wave clock pulses for all six motor channels under manual control. This is not used when controlled from a computer, which instead, leaves generation of this signal entirely to software.
The original ETI article does not mention anything about the frequency of these manual clock pulses, so I decided to do some research. I made some measurements of this signal using a digital oscilloscope with my unmodified board:
In my case, the manual clock oscillates at 72.46Hz with a pulse period of 13.80ms.
Adjusting the resistance of PR1 changes this frequency, and of course the resulting motor speed.
It should be noted however, the output frequency is technically determined by the capacitor and resistor combinations of R4 (39k), PR1 (100k), R5 (68k), and ceramic capacitor C2 (100n). This is collectively known as the RC (resistor-capacitor) tank circuit.
At the slowest setting, the frequency measurement is 34.9Hz with motors turning, whereas the fastest speed is 72.46Hz, so it would appear my motor driver board was set to the maximum speed possible.
There would appear to be no setting that results in any motor not moving at all, so it shouldn't matter what setting you start with. Providing IC6 is not faulty, and you've checked the other components associated with this part of the circuit, any driver related issue under manual control is unlikely to be timing related.
Providing the clock signal reaches IC2b (pin 11) and IC3a (pin 2) for each channel when switched to manual override, any driver issue is unlikely to be related to these timings.