[feoren]

The longer the centrifuge arm relative to the length of the projectile, the less of an issue this is. We're already talking about an extremely long centrifuge arm.

Attach the payload at two points in a narrow V, equidistant from the center of mass. In the instant before release, fire pistons that slightly extend the upper arm and retract the lower arm, applying the exact amount of force you pre-calculated was needed to counteract the differences in rotation between those two points. Release while this (hopefully uniform) force is still being applied.

Yeah, you're jolting the hell out of your payload, but that's peanuts compared to what it's about to experience anyway.