Here is what Terry Brady ...
2005 600-Yard IBS Shooter of the Year had to say about moly removal:
"I use moly and clean every two matches. I don't brush much, and if I do, I normally use nylon brushes."
Since I shoot moly, my cleaning procedure is different than you'd use with naked bullets. I went to moly so I wouldn't have to clean during matches. Now I'll clean every two matches--about every 80 rounds. Here's the procedure: I put a patch of Kroil through the barrel, then wet another patch with Kroil, stroke it pretty good, then I dry patch it. Next I run a couple Montana X-Treme 50 BMG wet patches and I let that set for 5-10 minutes, then dry-patch the 50 BMG out. Then I put a little JB on a dry patch on a jag, and short-stroke about 6-8 inches of the throat area for about a dozen strokes. After that I push another Kroil-wetted patch through again, and then wet/dry patch to remove the JB residue. The last step is to run a patch with Kroil.
This complicated process gets the barrel clean but I've found it may take a dozen or more shots to get the moly back in again so the gun shoots optimally. If somebody has a better/faster way to clean for moly bullets, that doesn't require so many fouling shots, I'm all ears. I generally don't use brushes, but when I do, I'll use nylon brushes (except in rare situations where I really need to attack carbon in the throat). Bill Shehane was the one who suggested I use the nylon. With a nylon brush I will send the brush all the way out the muzzle and draw it back in again. With a fairly loose-fitting nylon brush I can short-stroke the throat area (you can feel it if it's getting rough), but generally that's not necessary, and, as explained above, I can accomplish my cleaning with patches.
Taken from 6mmBR.com. Hope this helps. Art