The only one i am very familiar with are Hillclimbs.
I was a hillclimber at a National level for a few years, though you will unfortunately not be very competitive with the NSX due to how they define the groups.
I am about to get my track car log booked again, though i imagine i will go up a group from the group you would be in (Sports cars over 3.0L). Your main competitor would be a 600HP RX-7 FD, and a very skilled driver behind the wheel.
The sport is not for everyone, very little track time but done at 100.00%. If your keen to go to one let me know and i will come along with the MR2.