After working both NFHS and NCAA games, I appreciate the system that is in place in college games for handling the balls. Both teams provide their balls to the officials in bags. The officials control the balls from the moment they receive them until game management retrieves them at the end of the game. The officials then test and choose 3 balls that are within specifications. There are at least 3 ball people at the game, 2 on the press box side, one on the opposite side (though 4 is ideal). Each person handles the balls for one team.
On all changes of possession, a ball will come from the press box side. If a ball goes out of bounds on the opposite side (or ends up in the opposite side zone), the new ball will come in from the opposite side.
In HS, this can be modified by having ball people for both teams on both sidelines (one person from the away team is on the home sideline, one person from the home team is on the away sideline).
At halftime, the ball people give their team's balls to the officials. The officials will give the ball back to the ball people before the start of the 2nd half. Maybe this will not be realistic at the HS level, but the college system for ball handling makes getting new balls in the game quick and efficient.
If all balls are given to the officials before the game, with the ball people then using the approved game balls, then the officials will not have to deal with an unapproved ball entering the game.