Here's the thought I have often had about the alcubierre metric--
You dont need full negative mass, per se, at the aft of the vehicle. You just need a slight reduction in the vacuum energy at that location, and a slight increase at the front. Amusingly, this could help with the "Hey, you are gonna freaking ANNIHILATE whatever planet you stop at bro!" problem that the alcubierre metric supposes will happen, since the combined potentials of both lobes of the metric equal zero, and the "effective" negative mass at the aft of the vessel will magically just vanish once the device is turned off.
You wont get the "Instant accelleration" that you get with the full alcubierre metric based warp drive, but then again, we arent talking the degree of distortion that alcubierre described. We are talking a very small distortion. That means the drive is only capable of sublight travel, which makes it comply with all the causality rules we have come to know and love-- but it may be capable of giving us a sufficiently large percentage of C in terms of total velocity en-route that interstellar travel is possible without using generational ships by exploiting the time bending effects of special relativity. (However, we would need to be shooting a freaking lead torpedo to do that, since every little hydrogen atom the vessel came into contact with would have absurd amounts of energy applied to it by the collision with the vessel, and that means crazy radiation on the bow.) Something like 80 to 90% of C would be quite workable for interstellar travel, IIRC. One-way trips, but still doable.
(explanation: Basically, "normal space" is filled with little energetic particles that jump into and out of existence from spacetime itself. These little bursts of particle-like phenomena are known as "vacuum fluctuations". It is presumed that this device works by pushing against these particle-like phenomena in the very tiny period of time that they exist, imparting a momentum to them, and in turn, imparting a momentum to the device through the second law of motion. It makes physicists angry, because the vacuum fluctuations then disappear back into spacetime, apparently carrying this kinetic energy with them, and go POOF, leaving no exhaust. That means energy is either disappearing, or some other major violation of conventional physics of similar "Noooo, that kind of thing does not happen buddy" type thing. That's why the emDrive keeps getting poo-pooed by the physics community, despite the now interesting emperical test data surrounding it. However, if the energy imparted to the virtual particles (vacuum fluctuations) has some impact on the total rate of production, or total density of, these virtual particles between the bow and aft of the device-- then you would end up with something resembling the alcubierre metric, simply because the virtual particle density is a measurement of the energy found in the spacetime at those locations. The device might be working as a kind of "Heat pump" to move energy from one part of spacetime to the other. This would result in a pocket of spacetime with fewer such particles in it (negative mass in comparison to the spacetime outside the pocket!) and a pocket with more such particles in it (increased mass, compared to the spacetime outside the pocket), which when combined, equal zero. The degree of the "negative mass" curvature would never reach the kinds of values described for the FTL drive version-- which would require exotic matter of some kind that exhibits genuine antimass, but it would give you a "negative mass like term" for a weaker version, which makes this finding very interesting to me indeed.)