It would seem wiser to upgrade the turntable.
With a 4k budget there’s plenty of chose from, including other Regas.
For what it’s worth, I recently heard one of the skeletal Rega decks and was pleasantly surprised at how it seemed to sound like high quality tape.
Surface noise, what surface noise?
But there’s lots I haven’t heard recently - Technics would be another deck to look at as well the Clearaudio you mentioned.
I simply wouldn’t bother trying to mod the Rega, unless you wanted to change the motor, the arm, the platter, the plinth etc