As far as I know, and have done in the past, is to fit a Lister HR2/3 starter motors to Lister JP engines, since the gears are the same as the JP on the HR it should fit with out any issues considering the correct rotation is used, the mounting bracket should be the same as well although a spacer ring may be required to set the motor at the correct depth for the ring gear on the flywheel.
One thing to check for that no one has stated yet is are you sure the voltage is correct for the motor, Some motors I have seen fitted to the JP range of engine are 24V rather then 12V since these are big engines the 24v motor requires less amps than a 12v motor and hence means the wire used can be of a smaller gauge then if it were 12v, there should be some numbers stamped on the motor casing, as well as a rotation arrow to denote the rotation that the motor is turning, If you can find them and post them here or even a photo of these numbers and a general photo of the motor I am sure we can tell you what motor you have currently fitted to your JP2.
Some times I have seen a Lister S series motor fitted to the JP range and these can do the job but are under-powered for the task.
the other option of course is to just stick with the hand starting, no more electric starting issues.
LW