tilting left and right on the control could make your downed player tilt on his respective hips (rolling on side).
As in Pride FC for ps2, I thought the direction control wiggling was pretty decent for getting your mounted player into the guard. Expanding on that idea with the controller tilting (rolling on hips), and weight-shifting with the R analog stick might make for interesting position changes.
If, say, you are caught in a side mount, you can tilt your control to lean on one hip, and mash maybe a direct on your "D" pad to slide your knee between your opponent to get into a half guard position. Continuing to do this can switch you into the full guard position, for example.
If you are the one on top of a side mount, you should be able to shift weight in a similar fashion to maintain your position, or to try to full mount if you wish.
Ideas keep coming into my head about this...seems interesting.