Seems like there is already a mechanism, sans moving parts, of generating force post-launch. Not saying it is sufficient to correct a ground-launched, ballistic projectile though.
> A solid rocket almost certainly will spontaneously RUD when heavy acceleration is applied
I am skeptical that there is no chemical propellant capable of resisting the initial acceleration. That seems like a bold claim.
What about gas-based thrusters(i.e. ion drive with xenon or even just nitrogen gas)?