The amount of belt slippage you have will substantially reduce the power transferred to the pump. After it has been running for 10 or 15 minutes, and you have been activating it a few times, how hot is the small drive pulley? If it is hot, you know you are losing lots of power right there.
Secondly, since you replaced the motor and have cleaned and oiled it up, the problem would logically be one of those 2 things. Cleaning and oiling doesn't logically fit, so that leaves just the replacement motor with slipping belts. I would measure the belt length you need and go get a new matched pair of belts.
They sell matched pairs for a steeper price than singles, but that is what you need. If they don't have matched pairs, have them measure and pick the closest 2 belts.
You could try belt stick, but that is not the right cure for loose belts.
Tom