Harry may lose in the sense of failing to keep Hermione out of Azkaban, but I doubt he'll choose to lose. The lesson of the first potions class was not to get caught in a status/dominance fight at the cost of important goals. The lesson on losing in the Battle Magic class added "how to pretend you've lost without giving up any important goals." Losing in this case does not mean sacrificing "Hermione's comfort," it means letting his best friend die slowly.

The line about seeing the Wizengamot as PCs vs. as wallpaper and the final lines about Harry's knowledge of wizarding laws and culture suggest that Harry's solution is going to fall within the law and custom of wizarding society. Harry has already decided to undermine the political stability of the country because he objects to said country on moral grounds, but he won't do it now because it isn't time yet. As for sacrificing his humanity, I wouldn't want to bet on his ability to stay human with Hermione dying in Azkaban.

Losing and begging sounds far superior to most of the other options considered; the prospects for success may not be greater, but the loss if he fails is little.

Unfortunately he's gone Dark, and his dark side doesn't seem to know how to lose.