I do not expect the encoders to cause a problem like that. It sounds like your load might be causing the system to bog down at low duty cycles. You might consider a higher gear ratio motor, which would probably be easier to control at lower speeds.
Additionally, it is hard for the jrk to do feedback when the numbers it is working with are so small, and so it would probably be better to increase the PID period to something like 100 ms.
Also, it looks like you are not taking into account the gear ratio of the motor in your calculations. The encoder measures the motor shaft, not the output shaft of the gearbox, so you would need to multiply by the 4.4:1 ratio of the gearbox.