The repeatability of your probe can be affected by the spring pressure, the length of stylus and the orientation of the probe when the reading was taken. The spring pressure can be low enough to allow a reading without a false trigger - that means anything on the machine that can cause a vibration likely to dislodge the seated stylus without the stylus hitting a correctly targeted surface. If you have a mechanically quiet machine there is nothing to stop you using a much lighter spring pressure like those in a CMM.

A probe with a kinematic location, the three point contact system you describe, will have a different lateral spring pressure according the direction of probing. That said, if the stylus is stiff enough then the repeatability should be slightly reduced at the high points of the force compared to the low points around the 360 degrees of the X-Y plane. In the Z direction the repeatability will be improved because the stylus is acting as a column, and consequently much stiffer than in the X-Y plane. The spring pressure in Z is approximately four times higher in Z than the X-Y plane - the spring is acting only in compression, and not being tilted sideways as the stylus pivots on its fulcrum as in an X-Y move.

The key to accuracy of measurement is a repeatable starting point. In a machining centre the probe is usually anchored by a spindle orientation system. That means that if you use the same contact points in measuring a surface that were used when the probe was calibrated the the readings will not vary by the effects of lobing from the kinematic location - so keep things constant. If you have a cable-attached, manually loaded probe then always use the same position of the probe in the spindle and your readings will become more consistent which is improving repeatability. I haven't seen a probe that uses an arm that stops the probe in one orientation - but an arm like a tapping head or a boring and facing head uses would do that. That would leave spindle run out as a an error - I don't think high speed spindle (routers?) have spindle orientation methods.

What's left then to cope with is the error of centre line of the spindle to the nominal centre line of the probe tip. So, if you bore a hole in a piece of material you will have the X-Y co-ordinates of the hole. Without moving the machine, lift up the Z axis and swap the boring tool for the probe. If the probing routine can tell you position as well as size, then run the routine and see what the errors are between the true spindle centre-line and the probe's version of that centre line. Those values are the X-Y displacement of the probe stylus. If you can store those you can then use them to compensate for positional readings when setting work co-ordinates from the probe values.

You could try lubricating the contacts instead of abrading them. I don't know what with though - the contacts must pass current when the probe is seated. The oil should prevent the contacts from arcing.

Cropwell: I have some QTC 'tablets' somewhere - for exactly the same thing. But I was concerned with hysteresis on re-seat - basically would the stylus go back to the same point after triggering. I've no plans to go back to that project though.

Neale: I can't see why 0.020 mm can't be achieved - but that is accuracy, and a probe can only be repeatable - it has no accuracy as such of its own. So the 0.020 mm is a function of the performance of the machine and CNC system. As for thermal stability over time you are, in my view, spot on. In that case it doesn't matter how good your probe is, thermal drift will affect the readings.

Good luck