I quit using anti-seize on barrel threads, and I wouldn't use it on lugs for the same reason. No matter how careful I was, that damn stuff got on everything, smeared, hard to clean off, etc. I use a red high pressure grease on barrel threads and shoulders now, and the stuff Kelbly sells for lugs. One small dab on each lug at each relay. I know it has to go somewhere, and I use those dental rolls on a stick to twirl around up in the lug area.
You want something to stay put, use chain saw bar lube. That stringy stuff sticks to everything. Aside from a saw, I use it on my lathe ways.