Several British gunmakers operated their own "Shooting Schools" with creative target presentations, esp. "high pheasant" incomers
Charles Lancaster's "Stonebridge Park"
The nattily dressed Dr Wonko and his gun and shell bearers
The earliest U.S. clays "game" I've found it this:
Sporting Life, December 5,
1883 “A Walking Shooting Match”
At the great clay pigeon tournament in Chicago next May, match No. 6 for the Ligowsky sweepstakes, entrance $5, double birds, fourth notch, is to be shot under the following novel conditions: Five traps screened to be placed at irregular points in front of the score, which must be placed 30 yards for farthest trap. The trap judge will prepare 13 strips of folded paper, containing each a number from 3 to 15 respectively, from which the shooter will draw one slip, which the judge will privately examine, and allow the puller only to see. The shooter is to walk in a general right line, from the score toward the traps, upon receiving the reply “yes” from the puller to his query “are you ready?” When the shooter is underway the number of steps indicated on the drawn slip, the puller will pull any two traps, one after the other.
