My experience is the same as Beale - same problem, same cure. Savox servos on 1S and Spektrum receivers in general seem to be the cause of 95% of all the poor electronic performance I see.
Capacitors in the receiver will only offer minimal voltage storage, so they can help prevent receiver brownouts or transponder miss-counts. They cannot provide anything like the voltage or current needed to power a servo.
All the HW speedos I have had provided ample volts and amps from the BEC. They either work or they don't. Try Beale's suggestion first and see where you get to. HTH