A induction start motor has no start capacitor. A split phase motor is a poor motor, it has two windings start and run. The only way a split phase motor can start is by a phase shift. On a induction start motor the start winding are of higher resistance, longer copper and smaller than the run windings. On start the start winding will pull higher amps(LRA) and cause phase shift.
If you add a start capacitor it now becomes a capacitor start/induction run motor.
Also Wes I have to disagree with you on:
" Also, the "klixon" used with standard starting components is an overload, not a relay."
The klixon is a switch(relay). Its job is to take the start winding out of the system. If the klixon fails the start winding will stay in the sys and the start winding will stay in locked rotor amp and overheat. The overload then will shut the motor down. Now how the klixon works is it heats up and stops passing voltage to the start winding.