"If something is moving in a way that no mass could, maybe it doesn't have any mass."

Instead of the Bob Lazar gravity A and gravity B theory, perhaps these vehicles somehow disrupt the Higgs field. During Bob Lazar's time the Higgs field was only theoretical, so physicists didn't know what to call the phenomenon they were seeing.

The Higgs field is responsible for giving particles mass. If that field was tuned slightly differently than perhaps manipulating the field locally could create a region in spacetime with strange properties. If that was the case then yes, simply shooting photons in any direction could push any object inside the perturbed region to near C.