I've autocrossed mine twice. Once on said Chinese tires before I had my Koseis and Dunlops, and it was pretty neutral, it did what it was asked to do. Low grip levels, of course.
Second time was on the Star Specs, and I think I did have the sway bar on it. But it was in the rain and just slid all over the place. The alignment is weird. That's something else I need to have done. Star Specs aren't bad in the rain, so I'm attributing part of that to the alignment.
What kind of tires do you have? I just ran the Civic with low pressure for the first time and it was awful, people even told me they saw the sidewalls rolling over. And that was 30psi. I wouldn't do less than 30 on the front of the MR2. I'll probably start off with something like 34/38 F/R at this next one and see how the balance is. 35ish front and rear has been the sweet spot for the Civic. I've ran around 40 before but I see the center tread is wearing really badly because of it.