Most likely the RPR Chamber is slightly larger at the case head area. And on the MRAD, it's tighter chamber. You would need a small base die. Or have a gunsmith open up the chamber a bit (0.001"-0.002"?) at the 0.200 (case head part of the chamber).
Also, try Lapua brass...might mitigate this issue better.
I had a similar issue on a 6.5CM match chamber. ADG, S&B, federal brass all did this after a few firings. Lapua brass worked like a charm.
I was thinking of trying some lapua brass.... challenge is finding it. I'm stacked pretty deep of ADG so I've never sprung for lapua. Will keep an eye out though.
I also decided to shoot barrett an email for their thoughts so I'll be curious what their response is.