SoundSmith. Don't be in a hurry, but you will get a great rebuild. IMHO
Has Peter come out of the hospital from COVID?
I think you made a better choice going to VAS after recent examples of things I've seen from SS...especially if you don't want a perfectly good cantilever ripped off and replaced with a glued on cantilever/stylus assembly (cheaper/easier) in an attempt to renew a good sounding cartridge.
As I understand it doing a quick search, the Syrnix PU3 Arm has a hardwired Phono Cable, so no changing that without modifications. I wouldn't now suspect that being the source of Hum-Noise provided it is intact.
If there is a ground connection problem with the arm or motor then that can cause noise.