Bobby -
Start capacitors were used on many 3-speed motors, and on large capacity models, however I have not seen a standard capacity machine with an original equipment capacitor start motor.
If your motor is bogging down in pump-out and especially during spin, I would say it's time to have the motor serviced (find a shop that rebuilds household motors - I used one which specialized in pool pump motors) and they can diagnose and repair the old motors.
If you're willing, a standard Whirlpool 285222 motor should bolt directly into your machine. They do not look original, however the machine will function properly. There are some used on ebay for $18.99 plus shipping, and a couple new ones for $50-$55. The 285222 motor fits virtually all Whirlpool/Kenmore belt-drive machines and replaces single and two-speed motors. It can replace a 3-speed, however the extra slow setting isn't there.
If this were my problem, I'd buy one of those $18 motors or find one locally, install it so I could do my laundry (very easy swap) then take the time to find someone to rebuild the original and re-install it at a later date.
Gordon