I don't mean to be rude or disrespectful, but I have no problem playing off the mats, which require a different ball approach than when hitting off grass/dirt. I can land the ball with little to no roll out off mats. For me, the trick is to pick the ball clean off the mat, and use a high lofted club. Have you tried that approach? That said, I agree with you that if you try to take a conventional approach that would, in grass, leave a divot after the ball's lie, then you might have trouble with mats.
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