Hi Nick.
Motor problems are a large portion of HVAC malfunctions. Noise or slow star-up could be a weak capacitor. Static testing - where you disconnect the cap and test it separate from the system - doesn't always show a weakness. Better to do a dynamic test, with the cap in the system with voltage applied under load. (I only learned about this test procedure a few years before getting out of A/C. I don't feel like I cheated customers for all the prior years because swapping out a cap was really cheap, just to be certain). Several companies I worked for after closing my business had mandatory (static) testing of caps on all units we serviced. I would also do dynamic testing on many of those - and I found alot that failed the loaded test even though they seemed fine when static tested. (Accuracy is key - this is one job that really needs a digital test meter). Here's the procedure:
https://hvacrschool.com/wp-content/uploads/2017/06/How-To-Test-a-Run-Capacitor-Under-Load-1.pdfAlso beware that the + or - 6% is manufacturers imposed tolerances, not really application guides. They test a handful of caps out of every hundred and - if the rating they measure is with the 6% either way - they sell it. The insulation in modern caps is super thin, and go weak all the time under heat. You could install a say 60mfd cap, and it could really be 6-10% low (say 54-56 right out of the box) yet your motor NEEDS the 60. (That's what the engineers designed it for). Try to find a cap that is as close to the label rating as you can. Brands change all the time - I liked AmRad:
https://amradmanufacturing.com/Check all the power wiring and switches supplying the motor. Low voltage can adversely affect start-up torque and overall performance.
Lastly, could be worn/bad bearings. If the blower motor is more than 5 years old - and hasn't been oiled - could be the bearings are giving out. I know most motors claim to be "permanently lubricated", but that's misleading. So long as the motor lasts past the warranty period the manufacturer is off the hook. Even "sealed bearing" motors can be opened up and lubed. I pop the end caps off ( the forum member selling the mini pry bars has the right idea for this!) to expose the sawdust gland reservoir and bearing and put 10 drops of my Supco/Turbine oil mixture in. I have had only one motor in 14 years go bad for bearings after lubing with my brew. And I even brought back a few motors that were stuck - but I got to them before the windings overheated and my mixture freed the bearings and they started spinning again. The Supco 88 oil additive is superb - been helping me save anything that uses mineral oil. I even put it in my old Toyota!
Here's the link about Supco:
https://supco.com/web/supco_live/products/S8.htmlLong winded but hope this helps!