I played the ATA game as well as bunker trap (international) for many years and got pretty good at it. The most helpful thing I did was sub gage practice.
I stepped down to lighter, faster loads, in 12 ga. Standardizing on a 1300 FPS speed with various shot weights (very much like the mandated international trap loads back then) For all my ATA and live bird shoots, most using 7 1/2's. To furthur tighten up my game, I installed choke tubes in my favorite 20 ga dove gun, added a lace on comb, adjusted the pattern, and kept right on grinding birds. The practice helped my wingshooting a bunch, too.
I worked up loads, in each ga., to the 1300 FPS stadard. Magically, all my leads looked the same, no matter what gun I had in hand.
A friendly bet with a shooting buddy showed me that a 3 inch .410 was every bit as deadly on hand tossed live birds, as my 12 ga boomer. (closer and slower targets) I started shooting the .410 from the 16 yd line, just for fun. I got pretty good at it, and was once protested out of a win in a club match, for unfair advatage... (I won the "step back" shoot off from the 23 yd line)
I still shoot the mouse guns at fun trap, mostly 'cause it's fun and CHEAP. Shoot what ya got, have fun, be happy.
I taught both my daughters, as well as the grandsons to shoot trap with the 20 and they all still shoot. When they come to visit we always drag out the mouse guns and the hand trap for a family shoot off. My hair is gone, so is my jump shot. Them durn kids are getting better every year...
Paul