Well, at least now I know that my method isn't entirely unorthodox. Now if I could trust that my shooting actually reflected a problem with the sights. . . .
On that note, I took a class this past week and got in a little shooting off the clock while everyone else left for lunch. At this point I'm pretty confident that the sights are properly regulated. I actually turned in a decent group at 25 on just the backer, somewhat rapid fire (no lowering the gun between shots). Kind of surprised me, because I didn't have anything to present a specific aiming point. Maybe having less to overthink helped, and I wasn't ambushing a specific holding point.
I also had the chance to shoot an M&P with a fitted barrel—I didn't shoot it any better than mine with the stock barrel. I shot them one after the other at ~12 yards, and actually shot a little better with mine. I seemed to have been having a good day and put 8 shots in a paster at that distance. I shot similarly with the fitted barrel, but the group wasn't as tight. I wish I had shot the fitted barrel at 25, where it may have proven its worth, but I didn't get the chance.