Gateway is a great facility that has served us very well. The timed track time, test and tune autoX, and then drags would be my order of preference.
If Gateway says no to the 1/8 mile drags, someone mentioned on the Gateway Cobra Club Forum about possibly having a 200 foot timed acceleration and stop between the start/stop lines as another possibility that might work.
If Gateway says no to the drags in any form, and you just "gotta have one of those little slips of paper", there are plenty of dragstrips around all over the country that have test and tune days early in the season so that you can see what your car does. They may kick you out if you go under a certain time without what they feel is the proper safety equipment, so just do a few runs to practice your start and keep the terminal speed down. Then do one full blown run to get the slip with your time as they escort you off the track. (Not that I've ever done that myself, of course.
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I think that Gateway's central location and their experience with us is a VERY big plus. If you had it one year on the West Coast you would conceivably have to have it the next year on the "Right Coast" , and then maybe the Gulf Coast the next to "be fair". It may be a long trip for some of us, but to travel to the opposite coast would prevent a lot of us from making it back every year. It was a long drive for me, like John, but I enjoyed the trip there and back.
I guess what I'm trying to say is IMHO, "If it ain't broke, don't fix it."