I don’t think you understand – gravitational field propulsion isn’t just some idle speculation with the kind of glaring flaws you’re suggesting here; this has all been worked out theoretically, and there’s no debate that it would perform as calculated within the context of general relativity. So I can address your objections specifically.
First, it’s a purely geometrical effect, so once the system is gravitationally charged, there is no energy consumption (other than minor efficiency losses within the control system). Significant energy consumption only applies to reaction propulsion, like rockets and jets. And it’s not a matter of lifting something by placing a source of positive gravity above a device, or by placing a source of negative gravity below it. Gravitational field propulsion requires both polarities of gravitational field interacting with one another.
And we’re not talking about neutron-star magnitudes of gravitational field gradient (positive or negative), as your example suggests. It would only require gradients as steep as, for example, the magnetic field gradient of a pair of interacting neodymium magnets. Those are very strong, but they’re not nearly strong enough to tear themselves apart at the molecular level, as you described. With a relatively weak acceleration field of only one Earth gravity (aka 1g), such a device would reach the speed of light within a year. At dozens of g’s, like we find with rare earth magnets (as a strictly analogous example), obviously that time would be reduced dramatically.
And as long as you maintained a fairly linear gradient within the craft through proper engineering (or by confining the craft sufficiently far from the tidal forces as we see with the Alcubierre drive), then the craft and the passengers within it wouldn’t feel a thing – they’d simply uniformly “free fall” in the direction of acceleration. That’s why this model explains UAP maneuvers so well – what looks like dramatic accelerations of 100s of g's from the outside, involves no significant internal acceleration forces at all on the inside. Looking out the window of such a craft zigzagging through the sky, the world below would simply seem to zigzag around like a movie on the wall.
Such a device passing over matter, or landing, wouldn’t generate a field strong enough to affect the matter in any noticeable way – primarily because the field strength would only be high enough to support the weight of the craft against the Earth’s field of 1g, but also because as Usual Suspect mentioned the field strength would fall off by 1/r^2, where r = the radius of the gravitating element on board the craft. So operating near the Earth the effective range of the field is actually very small and fairly weak – unless it’s accelerating at 100s of g’s between the stars where there’s very little matter and it’s in a plasma state anyway.
