From your analysis it seems as if the electric pace motor is not starting up as quickly as it should.  Would an inline booster be helpful?

Ag Leader makes an amplifier to run electric devices.  It is attached to the PWM output of a module and uses a direct battery source to provide a high current PWM output to a motor. I have one at work and have bench tested it with a fairly large 12V pump.

Seems like we worked with a machine similar to this and had to use amplifiers with it.  It does seem strange that one channel is OK and the other is reluctant.