It's not lead fouling with a copper jacketed bullet. It's carbon fouling. Often times running a higher pressure will result in less soot in the bore. You might have to change to a faster powder to keep your load at that velocity and eliminate that. However, sooty powder fouling is no big deal in my opinion. In a .223 AI I had a load with H-335 that shot very well for 5-10 shots, then opened up to about an inch. You could put 100 rounds through it and look down the barrel and it would be mirror bright. One day I gave bl-c(2) a try and suddenly the gun would shoot .5" five shot groups for 100-200 shots without cleaning. One shot and the bore looked filthy. The deal is, that sooty carbon shoots out instead of building up. That baked on carbon that makes your barrel look clean can sometimes wreak havoc with accuracy as well as be very difficult to scrub out. It depends a lot on the powder. Oddly, H-335 and bl-(c)2 are the same powder, separated out into two separate canister grades. The faster lots get labeled h-335 and the slower lots get labeled bl-(c)2. For them it was simply that high pressure loads causes a powder fouling that looks good, but causes problems. Low pressure loads cause a fouling that looks bad, but does not cause problems. I've found with RL-15 that in spite of leaving the barrel looking clean, I never have the issues that I do when shooting high pressure loads with H-335. I can shoot 3-4 f-class matches without cleaning.
It's not lead, its carbon. It's not hurting you on a hunting gun, and if it were match gun, I would let the paper tell you if it's a problem. Sooty carbon in the barrel is not always an issue. In fact, it usually isn't.