Right. As I understand the problem, there is enough fuel to accelerate to speed, but not enough to slow down. I am just wondering if one of your characters might have a sudden insight into being a lot more efficient with the fuel before getting up to speed. Or combine that idea with the others here. It doesn't necessarily have to be one idea that fixes the problem. Kind of like that scene in Apollo 13 where they route power through a sequence to be more efficient.
Hell, the last time I took physics was in high school twenty years ago.