Running cap is for AC motor. Speed control of DC motor is thru limiting the current using a resistor.
+1 on resistor. Replacement motor might have outside tolerance the resistor could not take. Extra current is heating up the resistor cooking up the insulator..
Metal clip of the blower is for balancing. Bring it back to EDS, have the seals re checked. Sounds like youre leaking capillary oil or refrigerant somewhere in the evap.