Haven't looked at every box score, but I'll throw a few theories out here...
Four of your seven perimeter defenders have defensive ratings in the 30s. That's almost assuredly playing a significant role in the issue. Along with it, your IQ's, while not horrible (everyone is a B or better) are missing the elite A+/A ratings which really help in the press. That might be having trace effects, especially in road games and vs. higher IQ offenses.
Beyond that, a few other things that may or may not be contributing to the issue or which you may want to ponder...
-- You didn't mention if you're using target minutes or fatigue. I assume fatigue, but if you're using target minutes, having players set to "take out quickly" could be a contributing factor with players being overtaxed in the second half to "catch up" on minutes needed to make their targets. If you're playing with fatigue, what level do you have them set to be removed at?
-- Have you experiment with other foul settings (normal or leave in longer)? It could be that part of your foul issues are coming because players are playing into higher fatigue levels to cover for other players who are being protected due to their foul status.This would make the ones in the game more prone to foul if they're playing at yellow/orange/maroon fatigue in games. Even though it might seem oxymoronic, it might be better in the long run to set players to normal or leave in longer (I've used the latter setting exclusively for probably 40+ seasons)
-- You've played a number of close games that you lost and a couple more that from the score indicate that you may have been trailing late before winning. How much of your foul-out issues have come during the flow of the regular game vs. intentional foul situations in the late game (which almost always will be rung up against a perimeter defender)? Is it possible the "problem" is an illusion created from unique end-game situations?
-- Your press team is committing less than one foul more per game than my team (Missouri-St. Louis, same world) is and we both appear to be running a 7-4 setup for perimeter-post. I find that 20-21 fouls per game is what my teams tend to average per game over the course of a season running press at D2. Our starters are playing an almost identical number of minutes, so again I'm not seeing a glaring issue there that jumps out at me and screams abnormal.