I would imagine that they don't have very good high speed control, stock. Probably as the big SCT chassis acts like a huge wing, so when you accelerate, the rear end goes down, front end comes up (easy physics!), and then you have a ton of surface area to create lift. This could probably helped by adjusting the suspension to a "speed run" style, which is to say, when the truck is stationary, with the battery in, the front end of the chassis is a little lower than the rear, so when you accelerate, the chassis is about level, instead of leaning back, creating lift. And as you said, the body is gonna have to be one of the first mods, I haven't driven and SCT before, but in videos, I can see that "parachuting" effect, and they blow over, catch wind, and handle jumps badly, especially bigger ones, and the moment the nose goes up and air gets in, your air control pretty much goes out the window! Some people like to "vent" their bodies, as you know. Basically drilling and/or cutting holes and slits in smart places to let some air come out. If done right, it'll handle better, but you'll always have a "little parachuting".
I'm wondering if a front splitter/wing would help to with some front-end downforce, as on the Slash/Bandit/Rustler, there's significant "backsweep" (for lack of a better term) on the front A-arms, so the front arms can act like mini wings too, if there's enough surface area on the bottom of the front A-arms.
Traxxas tried that idea here, the front splitter didn't really help much, but food for thought! A wheelie bar would also help, I'm thinking a short wheelie bar, or none at all, for street ripping, and a long, drag style on for those crazy 6s speed runs.