Keep the Rega and ditch the Strathearn - they were seriously flawed by design - a low torque Direct Drive that was troubled by the extra stylus drag of low frequencies!
There could be a number of reasons for the Rega's speed inconsistencies. Apart from the bearing (with the platter on and belt disconnected it should spin for over a minute with a gentle push), check that there's no grease on the belt, motor pulleys or the outside of the subplatter. Download a strobe disc from this site and check the speed under electric light.
Let us know how you get on.
Technics SP-10mkII/SME 345/Clearaudio Victory Lo/Rega R200/Shelter501mkII, Whest PS.30RDT, ifi iPhono.
Cables: wire coat hangers.