I used to autox my NSX regularly up in the Seattle area. I had some very fast Porsches to chase in ASP, prepared by perhaps the best Porsche guy in the US, Greg Fordahl of Fordahl Motorsports, and driven by some very good drivers. The Seattle area has almost as many national champs as SoCal / San Diego.
I was at the point where on a good day I could get within about 2 seconds of the Porsches on a roughly 60-second course.
My car had off-the-shelf Koni's, Ground Controls with 325/425 spring rates (I had 450/550 for a while but that was too stiff). Dali race sways (22mm I think), 15/16 stock wheels with 225/50/15 265/45/16 V700s (fronts were used, which didn't help). I found my biggest problem was front end grip on low-speed corners. The car could start to get a little over-steery in slaloms, and very understeery in slow corners, but it rocked the high-speed corners because of overall grip and speed of weight transfer. My car was also set up with too little rake. I think if I autocrossed my car now (front end is MUCH lower than it used to be, and the car has way more front-end grip now), it'd be a whole different ballgame.
To truly make the car good in ASP, you'd have to:
1) get a 97+ coupe, or update the motor and tranny if they're listed on the same line (last I checked, the NSX wasn't even explicitly listed for ASP)
2) build the motor to the extent of the rules
3) get 17" wheels / tires with hoosiers
4) get some penske / JRZ / moton shocks and someone who knows how to tune them.
5) hard bushings throughout the suspension, if in fact that's legal for street prepared.
6) reduce as much weight as the rules will allow. Removing A/C and doing race buckets would be a good start.
You'd have a really good car if you did all that besides the motor. The motor would be the last thing if you were really going for national competition, or just had too much money to play with. Some of the normally aspirated tuning stuff that Science of Speed has been working on would probably be Street Prepared legal and make a big difference.
The gearing does hurt the 5-speed NSX quite a bit, on some courses. However, I've seen many courses where the tall first gear actually gave me a good advantage because I could take like half the course in first gear. With a 5-speed NSX, you definitely have to get good at downshifting for the slow corners.
Re-packing the stock LSD so it's a lot tighter would probably help quite a bit, too. The LSD basically didn't do jack in my car with race tires, and I'd lose quite a bit of squirt out of the corners because of inside wheel spin. There's a lot of room in the stock specs for LSD pre-load as well, so I'm sure it could be done with full legality. Stock preload range I believe is something like 50 to 115 ft-lbs.
I stopped autocrossing because the events got too full, and 3 runs was not worth being on site for 6-8 hours.
I live in Marina del Rey now, and I'd be interested in doing some autocrossing, but I don't know of any events in the area. I also have a friend who just moved down here (to East LA) who's quite an enthusiast (he has a Neon ACR with $5000 JRZ shocks).
I also disagree with the comment above about lower-profile tires not helping. It may have been my particular combination of car setup, wheels, and tires, but I found that running S02 pole positions in 225/35/17 and 255/40/17 yielding times pretty much the same as my V700s, because the car was much more precise and driveable. However, the 17" rims I had the S02's on were +38mm front and +43mm rear, so the large increase in track width, especially in front, may have also affected the comparison. Futhermore, the V700s I was running were a bit wide for the rims, which may have compromise their grip and handling characteristics. To be truly competitive, though, you'd definitely want hoosiers on 17" rims.
If the NSX is still classed in A-Stock, I think a 97+ coupe would be extremely competitive. Great power, great handling, and good gearing.
-Mike