Have a look at numerous Rega setup and service threads we've all contributed to. OLD Regas can run ever-so-slightly fast, although I think this was sorted some years ago.
The MAIN reason for slow Rega decks is that the ball is missing from the main bearing. The rounded spindle edge, coupled with the radiused bottom of the brass bearing "cup" means the bearing will run, but slightly stiffly, without the ball in the bottom.
EASY way to check this. Remove the belt, replace the platter and give it a little push. The platter should run for ages before gradually coming to a stop. Ball-less, it'll run but stop fairly smartly.
The ball is a standard size and Rega will probably post you one of you ask 'em nicely. A drop or three of EP80 gear oil, as Rega use, will ensure the next twenty years of reliability. The spindle tip should be clean and with little more than a tiny dimple on the end. Run dry for a while, the ball causes a very large concave section on the flat spindle-tip. No need for ruby style balls, the steel one fitted is perfectly hard enough thak you 
The bearing nut should be firmly tight - don't go mad - and the motor should be free to bounce around if original. The pulley sometimes appears to lean towards the platter slightly, quite ok, and vertical from the front or back and this can be carefully fiddled. The fixed motor of the 2000 issue P3 had a different circuit board, a circuit of which I'd like to see, as it could make for a cheap mod to the Thorens 150/160 motors too...
I can't go on and I can't go back, I don't feel so matter of fact,
I tried and tried to make good sense, What's the good to try it all again?