Mmmm I wouldn't focus so much on laptimes... that tends to get you into trouble
I can say that the mini was made for ringing. Both suspension and brakes are more then up to the task.
All that said...
With a margin for errors, not on the limit, normaly a bridge (tiergarten) to gantry (after galgenkopf) time of 10 min, 9:50 is normal for a cooper, I guess with an S you could substract at least half a min.