I'm more partial to Street Fighter it must be said, though I do agree with you that Skullgirls has more and higher-quality pure lore to work with. Street Fighter, much as I enjoy it, is kinda like Mortal Kombat in Tekken in that its plotlines tend to be when ya get down to it some ridiculously convoluted and absolutely mad set of reasons for why a bunch of people should punch each other. Many times. 

Not that familiar with the Skullgirls lore but I could certainly bone up on it if need be. Just the atmosphere of a fighting game is something fresh on my end, mind, so I'd be intrigued to see whatever you could come up with if you're pursuing the route of a semi-original background. :P

In short, I'm liking all of these ideas enough, and are pretty easy between 'em.