Two things. First, there's a bit of trick getting the pad under you lengthwise when you get into the hammock. You sit down on it and twist to bring your legs in, and the pad twists under you. You need to get stretched out and then work the pad to be in the proper position. And stay put. Any twisting and turning and the pad moves with you.
Second, you're raised up higher. That would no be much of an issue with the stock version of the BMBH because of its depth, but this hammock is shallow. That makes it more prone to tip. Look at the picture of Dutch an imagine him higher with respect to the hammock edge by 1.5" or so.
IMHO the pad pocket in the stock version of the BMBH is the perfect way to integrate a pad into a bridge hammock system.