Did you RM the ZR1 (GT Auto - Race Modify)? If so you have all the upgrades you need. I am not home so I can't give you my setup but this one is good:
http://www.gt5-tuning.com/index.php?...C6%29_RM_%2709
Try the first tune, ignore the HP just race mod the car, get racing softs and go with whats stock. The ZR1 RM is inherently twitchy this should settle it down a bit.
Throwing HP at street cars is a poor idea in this game they will never handle like the race and RM cars do. I have a GTR I use online a lot thats an absolute killer at 600 hp but I rarely run with more than 600 HP as any more than that its just too much of a handful even with AWD. I'm actually slower, especially on the ring with more HP than that.