Goatwuss,
The way the Well Tempered arm was set up, I had to completely change the way the cartridge mounted. Originally, the cartridge mounted to an aluminum crossmember, which in turn mounted with one screw to a slot on the end of the armwand. The threaded hole in the crossmember was stripped out to where there was play between it and the armwand. I changed it to where one of the cartridge mounting screws goes directly through the slot in the armwand, so that with proper torque the mounting is now very rigid.
So the answer is, maybe you need to do more than just tighten the cartridge mounting screws. If your arm has a conventional headshell, and the headshell doesn't fit tightly into the armwand, you may end up with the same problem I did no matter how tight your cartridge screws are. Seems to me everything from the cartridge all the way back to the bearings needs to be pretty rigid, whether you have gimbals, a unipivot, or strings like my Well Tempered.