Keep the Saw on my Left, Lanyard on my right- that keeps seems to reduce the nicks. Have my climbing line through a biner on my right leg, often times, which keeps it our of harms way ( I also run a spur through it less). I also tie the saw up if I'm not using it for a bit and I have some more technical climbing to do (not practical for removals). When the saws OFF, I disengage the brake - don't know if that helps.
I'm a dangler - especially on straight up vertical trees, on removals. I'll admit it...
I also replace my rope every 6 months, and have a tied, rather than a splice, lanyard (and replace that every 6 months). Wish I could splice!!! After 6 months, they definitely have a couple of nicks on them, but not crazy.
My groundman always puts the scabbard on sending the saw up the tree- I never did tho. He's a much BETTER groundman than I ever was!