Appears your shooting is consistent.

Now you need to work on concentration and focus to move up to getting them all. Best way to do that, is just as you were advised; "stop counting them". Stop thinking about "25-straight". Ultimately you don't want to miss all day, so just focus on breaking each bird... "individually". You can only break one at a time, so each time you mount the gun, only focus on breaking that bird...not the next ones, etc.

As to your flinch, something wasn't right in your sequence. Probably lifted your head a tad, or just your eyes even and that short-circuited your system. Some people are more sensitive to this than others, and it appears you may be more apt than others. I went 20+ years until I experienced these phenomena. I knew right away what happened, as I "peeked" (raised my head) on a straightway, and the gun wouldn't go off. So, I make sure my set-up is solid every time.

Most clubs have a shot weight (and size of shot) and velocity restriction. Dram Equ is actually a irrevelant number that's outdated since switching away from blackpowder. If you shoot better with faster shells at 16yd, that tells me you're shooting behind the target generally. No need to shoot a shell faster than 1150fps, at 16yds. 1oz #8 has more pellets than 1-1/8 of 7.5's with less recoil (generally).