I voted I left the score reels in place but I believe on the last one I did, a Grand Prix, The condition of the reels from the 4th player to the 1st player was night and day so I got really complicated and removed everything but the score reel switches from the backbox a pair of reels at a time and rotated them. So first player 100 points became the fourth player 100 points and the fourth the first and so on.
If I had any tip it would be to make sure your floor is swept clean before you start, them little clip rings have magic invisibility powers where they can vanish and then re-appear only after you give up, go for a coffee and then look for the other part you just dropped...<sigh>