Since you mentioned the wobble was the most objectionable issue, why don't you eliminate that variable with a better seat pedestal. Garelick makes a 4" pedestal series with a 12" base. It is as solid as a rock and rotates and slides as smooth as silk.
PEDESTAL BASES WITH 4 INCH DIAMETER POST - Garelick EEz-In
Then, if you decide you still need to upgrade the seat, you can do so at your convenience.