Since I use at least a 12 pound pedestal rest sometimes for target shooting...I prefer not to deal with a Lead Sled.
May I suggest that you stop cleaning the rifle every shot or two. That's where a clean bore can cause inaccuracy problems. I prefer a "seasoned bore" --- where I'll clean the bore after 17 shots without using oil. After the copper solvent cleaning process...I'll send a brake cleaner degreaser patch down the pipe. Then I'll crack-off one or two fouler shots to season the bore --- then I'll resume my target shooting for another 17 shots...since I know that accuracy degrades for a hi-power rifle after 17 shots.