If you're really going to run in one of the turbine classes, I don't see why you couldn't run a modified body, as "The body configuration is unlimited". However, you'd certainly have to meet all the safety requirements of the "Special Construction" category, which are extensive.
The turbine classes are based on vehicle weight, not body configuration.
However, as a USFRA Tech Inspector, I don't see why you couldn't run it in the World of Speed 130MPH Club, where the rules are minimal. See saltflats.com for details, but you'd need an approved helmet, tires suitable for 130MPH, and a few other odds 'n ends, but you don't even need a roll bar. The downside is that if you exceed 139.999MPH, you'd be disqualified. For this, you're timed in a 132-foot trap at the end of one mile.
But there's also the USFRA 150MPH Club. For that, you'd also need a minimum 4-point roll bar, a driver's suit, shoes, and a few other things. Here, you'd only be DQ'd for exceeding 159.999MPH. For this class, you get a 2-mile run, then you're timed from 2.00 to 2.25 miles.