So it turns out, before discovering the bug, I actually wrote code to find the optimal sequence when your choices are restricted to integers. I thought, along the same lines as you, "maybe if you burn 165 or 170 or something in the first non-zero term, then you could burn less on the 14 turn and still land."
And this is how I know it's not possible, at least with integer burn rates. :) I checked all 201^9 combinations, with a few optimizations to cut down the search space.
That's different than what you said, of using floating point for the last burn. But it is in a similar spirit.
