Mr. P, SCTA/USFRA does not allow jet bikes or rocket bikes -- for that matter, nothing that's thrust propelled. Turbines geared to the driveline -- yes, but pure thrust -- no.
Second -- weight is your friend at Bonneville. Lightweight usually means wheelspin. It seems that while the aerodynamic resistance increases exponentially with your speed -- your traction doesn't change, and at some point aero restriction exceeds the amount of horsepower you can put to the ground -- wheelspin results. Pin the throttle -- and your drive tires go immediately to spin mode. You don't gain speed, you gain tire heat, which, in turn, gains you blisters on the tires or chunks coming off the tires, which, further in turn, lead to tires going bad and you slowing -- or stopping in dramatic fashion. If you need to run where traction is better - you need to run at one of the venues that runs on regular ol' pavement. That sends you back to ECTA, LTA, Texas Mile, etc -- and NOT the salt.
As for why the trike wouldn't fit in the unlimited class is plain -- the rules don't allow such vehicles, unlimited or whatever. Check with the various committee chairs, listend in the SCTA rulebook, and see if they can help you find a way to run. I will add that USFRA will now and then figure out a way for an otherwise non-rule compliant vehicle to make a run on the salt, so maybe you should get in touch with Jim Burkdoll. He's their race director and club president, I do believe. Best wishes and good luck.