Not too surprised at the fouled rounds shooting slightly better... at least for a while.
When I used to do high-powered rifle shooting (smokeless, cal .30), we were allowed a couple of sighters after a couple of "fouling rounds" before shooting for record.
A gun will shoot differently whether it has some fouling in it or it is clean, so the first clean shot is here, the second, with a little bit of fouling is there, and sooner or later, the increments in fouling on successive shots get less and less, and the gun groups better (up to a point.)
Seems to me this process would be a lot quicker with King Black as opposed to smokeless.
Other processes which vary from the first shot can do the same thing, such as (at least in rifles), settling the action back into the stock better and better with each shot, and in BP handguns, backblast fouling can take up tolerances.
I have an M1 Carbine which definitely shoots better dirty, I mean really filthy, apparently for this reason.
One other effect, though it's mainly with rifles, is the greater heating with more shots. I had a Winnie .243 where the "one shot" groups were OK (meaning letting it cool off for ten minutes for each shot) but successive shots without cooling made it walk across the target.
Jes' my thinkin' on it.
Terry, 230RN