If your NT consists of player that tend to foul a lot, it's easy to see why your team as a whole would foul a lot right? If they already foul a lot, they might even foul more when playing in NT games because of the better opponents. If you don't think your players are injury prone, then we might have to agree to disagree.
Maybe you could experiment with playing other bench players, that are under 1.5 fouls per game in their regular games instead of the ones that average 3.