Though I solved it in 49 moves (yay me), I realized when thinking about efficiency, it didn't take into consideration two important things:
1) all of the turns I was making in order to be most efficient, whereas overlapping a few times would have probably taken less time, and
2) I spent a lot of thinking on the spot, as to what was the most efficient path, rather than moving the mower.. so while I only took 49 moves, the time spent on inaction may have balanced the scales with someone who just kept moving.
There's a life lesson in there somewhere, I'm sure!