Jed, that's a nice theory but is still flawed. The direction still has to be reversed at each end so the ever increasing forces will still cancel integrated over each period.
However eventually you would have pumped enough energy in for surrounding spacetime to collapse drawing the entire planet to a point. In this respect your distance would be reduced, although the long abandoned destination crushed beyond recognition. Unfortunately it would now take the remaining time of the universe for you to get there!
I would rather hitch a lift in a blackhawk vs a blackhole!
Jiff, i respect your tanacity. Please build the machine, since i suspect no amount of analysis will convince you otherwise. But, when it doesn't do what you feel it should, don't be disappointed. You will still have gained insight into the immense power of conservation of momentum (and energy, which just describes linear momentum though time dimension).