- Have you tried setting the new setpoint first?
- Have you tried just setting the new set point, leaving the PID coefficients the same?
- Have you tried just setting the new PID coefficients, leaving the set point the same?
The behavior in these three cases should give you a much better idea of what the problem is, and maybe how to solve or at least work around it.
Also, if you're driving to a position that requires some torque to hold, a P-only solution is destined to droop to the level where the output voltage is enough to hold the drooped position. Are you adjusting for this by making the set point higher than you really want?