I don't know why I didn't think of this before: two genres that are big in Japan but have pretty poor representation anywhere else: visual novels and dating sims. Visual novels play more or less like "choose your own adventure" books (i.e., user interaction is mostly multiple-choice questions on what to do or where to go next; most people don't consider these to be games, but hey, I like a good story), and dating sims, uh, play like simulations of dating. I think the closest thing I have experience with would be the recent Sakura Wars V release from NIS America, which combined dating sim elements with strategic warfare. The date thing in FFVII is also similar. Anyway, both of these are genres which almost never appear in the US, and I think SCEA actively tries to keep visual novels out of the North American PlayStation marketplace. However, if Minis are looser in terms of content policies, we could finally see if the market is willing to play these even if Sony doesn't think so.
Of course, making a game from one of these genres then comes with an element of risk. You might end up with rather poor sales. If you're going to make one of these, the story and/or characters will have to be really good to get people's attention and break the stigma.
Love the idea of a side-scrolling shooter featuring Ace Armstrong on foot!
Isn't that kind of game called "run-n-gun"?