You can definitely get a J360 fixed in the States, you just have to make a point of letting them know it's a Japanese unit, or they'll give you an American one since they usually just give you a random system while they repair yours. If it's a launch 360 tho, highly unlikely it'll be under warranty and probably isn't worth paying to fix.
Anyway, let's wait until Espgaluda 2 comes out before we celebrate region free games! The fact that they didn't want to give an answer during the cave matsuri might be a bad sign, although there's still plenty of time left before the release.
Besides, you might be able to play Cave games, but you won't play the upcoming game of the year "CHAOS;HEAD Love Chu Chu" on an American system!