If you could accelerate a mass without a recoil mass, momentum would not be conserved. Conservation of momentum is right up there with conservation of angular momentum, mass/energy, charge, baryons and leptons. In order to violate those laws, there would have to be variation in things that are invariant, such as reversal of time or travel faster than the speed of light. They are what defines our universe. Our universe functions as observed only because such invariances are true. Find a counterexample and, unavoidably, our universe would cease to exist.
And yes, zero point energy is there but it is not accessible since there is no lower energy region for it to move to. It is like having a thermos full of coffee all at the same temperature. Inside the thermos no work can be done since all locations are at the same temperature. There is no 'sink' for energy to flow to. It is the flow of energy that produces work. Work is required in order to move a spacecraft.
You are locked solid into the narrow range of everything, but everything, being relative to Einstein's observer standing still by the railroad tracks watching trains go by, else watching apples fall from trees and looking through his telescope. One already existing obvious "counterexample" is quantum mechanics which obviously does not function as observed (according to classic and relativity physics). The open systemic universe "at a distance," the probably unified universe, is nothing like the foreground, closed systemic, universe you seem to think the entire universe is tied to. I am of the belief that we are going to find it a very different universe out there when and if we get out there than the one you appear locked into here in the cave of Earth. There are going to be physics to it you know nothing of, physics even someone like me, and geniuses like Stephen Hawking when he was alive, only imagine or envision. It's going to be a vastly different world and universe . . . and physics.
"Reversal of time" is an observation a traveler of the universe always observes to his rear. Stealing your own example, it is why he, the traveler, would see Sol and Earth 4.27 light years away to his rear as he approaches Proxima Centauri by way of speeding, accelerating, up in the future of Proxima Centauri on the way. Always, always, by way of speeding, accelerating, up in the futures of his destinations on the way to them (from their past (-) to t=0). That he will observe his departure points in "reversal of time" is the exact recoil in time of that same speeding, accelerating, up in the future to the fore. The difference will always be his onboard clock time. The Earth-bound observer will never observe his arrival, no matter if it took him 5 days or 50 years according to his onboard clock, until 4.27 years have passed plus that traveler's onboard clock time, In other words, if it takes him 50 years to make his voyage, the Earth observer, relativity speaking (sic), would measure the crossing of space to have taken the traveler 54,27 years of time. The Earth observer would, if he could, observe the traveler to have aged only 50 years in that observed time of 54.27 years for the voyage. If it takes only 5 days per the traveler's onboard clock, that would be 4.27 years and 5 days observed by the Earth observer for a voyage of 4.27 light years (thus a travel 5 days in time less than the speed of light, slower than the speed of light . . . observed), and an observation that the traveler had only aged 5 days, that the clock had only advanced in time 5 days, in 4.27 years and 5 days of observation (if it were at all possible). Yet the traveler at Proxima Centauri observes an Earth and Sol in the distance that by relative observation would exist a little before his four years old child, four years old when he left Earth, was born. He traveled swiftly, very swiftly, into a future (+) in one direction, and recoiled, rebounded, just as swiftly, exactly as swiftly, into a past (-) in the opposite direction.
I, who have read, studied and thought on history, on change, and a future of yet more change, virtually all my life, already have children, grandchildren, great grandchildren, and still hope to see a beginning of yet another generation of my family, look forward to a great new outbound frontier of opening, a new frontier of universe and of physics for them. To me, seeing you naysay even possibilities, and providing meaningless closed systemic foreground-local proofs, too bad you don't, or can't see what we see. From your dead-slow and slower inertial universe life will be advancing into a lightning-fast almost inertialess, if not completely inertialess, universe. The unobserved
universe. The unobservable
universe (t=0) to the Earth-bound observer (t=0). The one, the many, always out front (t=0), to infinitely out front (t=0), of the speed of light. Macrocosmic, as well as microcosmic, distances essentially "quantum entangled" (t=0). The only frontiers (t=0), the only universes (t=0), that travelers (t=0) ever travel out into (the less, and ever less, relative, to non-relative, universes always out front of, always reaching beyond, the speed of light). Red and blue shifts of light help prove that . . . the distances, to vastness of distances, between realities (t=0) (plural) and relativity (singular). So does the principle of uncertainty; the principle of ever-growing uncertainty, prove it.