You should definitely check out "Tick Tick... Boom!" if you haven't yet! While it's not your traditional superhero film, it has that superhero-like feel of overcoming personal struggles. Andrew Garfield's performance is so heartfelt, and it really captures the spirit of fighting against the odds, much like a hero would.
Also, if you haven't seen "Super," it's a wild ride with a very unique take on the superhero genre. Rainn Wilson's character is far from the polished hero we usually see, and it gets into some pretty dark humor and thought-provoking territory. It's gritty and raw, which is completely different from the bright and flashy style of most mainstream superhero flicks. What unconventional films have you enjoyed so far?