Where is this 'contactor' of which you speak and is it accessible to some cleaning or maintenance?
Physically in the unit, not certain. On your schematic you posted near bottom right of the page is two boxes representing them, one for open (OP) one for close (CL) each has two "coil" terminals and 9 terminals for power leads, or three sets of COM/NO/NC contacts.
Most commercial operators I have dealt with they are usually easily field replaceable definite purpose contactor style unit. Residential operators it may be more of a PCB relay, probably because the residential ones usually have smaller motors and the commercial ones are big enough the PCB relays won't have heavy enough contact rating.
Adding more capacitance would increase phase shift and give the motor more torque. Too much will smoke it, though on a short duty cycle like this has there is a lot of in between that gives more torque but still will eventually end up with shortening life of motor. But presuming nothing is wrong and you do need more torque then what you have is undersized for the task at hand. before messing with the capacitor I would want to know if both motor windings are drawing current when this thing is not working. If one is but other one is not - I'd still suspect open relay contact that is supposed to be closed. Capacitor isn't that prone to being something that intermittently works relay contact much more likely to be intermittent. I say this because you said the motor hums but won't turn. If nothing happened at all, not even brake release, then the issue probably more likely in the control circuit.
You asked about RPM sensor as well. It doesn't show details of it, just the terminals that interconnect to the control circuit, they are on lower left of the first image in the post with two images.
