It isn't clear to me that the reaction wheels are for the launch vehicle and not an attempt to show the hater's that the second stage rocket will survive the launch. I'm 99% sure in their videos they're just flinging this dart out with no attitude control and letting the tail fins and heavy nose keep it from tumbling. At 1:58 it exits the tube pointing about 20 deg from straight in the direction of centrifuge rotation. And in the next 5 seconds looks like it pitches back almost the same amount in the other direction. I have developed no intuition for aerodynamic forces at mach speeds but I wonder if different things happen when you hit atmosphere at 20 deg of pitch at mach 6 instead of 1.6 🤔. I also love how he talks for a couple minutes about C_D improving between mach 1.6 and 6 while completely ignoring the small ^2 floating next to velocity. Also ignoring that C_D for a dart shaped body only applies when it's not sideways.
I think based on the discussion here it's unclear what the reaction wheels are for. I also think it's clear that they're very proud of making one. They themselves might not know what it's for. They will never breach Mach 1. They will never achieve a vacuum thin enough to do so, they will never achieve a rotational velocity fast enough to do so, thus they will never have to address the creation of a shockwave in their chamber, which is good, because it would be dramatic.