I'm still on a huge high from playing that storymode like 50 times. Big Band is excellent and I very much enjoyed him laying down the verbal roast on pretty much everybody, but Valentine and Double most especially. I also really liked that Lab Zero (the developers) finally got their shit together and made a storymode where every fight actually had context and plot relevance. Finally! Keep doing that, guys!
On the topic of Theonite: it appears to be the SG-verse's "Does Anything The Plot Requires Mineral". It powers the Skullgirl, Parasites have it and it's a component in Synthetic Parasites, it can be used to power time-warping devices, et cetera. If there's ever a need to explain how something mysterious works, boom, slap some Theonite on it and you got your reason right there, probably. "Theon", from the Greek "theos", means "god". More than likely, the stuff has a connection to the Trinity--theos can also be used in the feminine to mean goddess.
Also, I feel the need to point out that Peacock calls Big Band "pops" toward the end and that shit is cute as hell.
I think Squigly's story had more of an... epic feel to it? (I swear I'm using epic in the classic sense here, not the modern "omg lel so epic XD" sense.) Big Band's is the storymode that just makes all around the most amount of sense, but it felt... smaller in scope to me than Squigly's. Not sure why--maybe it's because Squigly's storymode like, immediately jumped into crazy amounts of action and didn't really stop for anything? Big Band's story felt a little more easygoing to me, I'd say.
Not that I enjoyed it any less. It wasn't as "hype", sure, but I love love love all the cameos that came up. There was a ton of character interaction and banter in there and it was just fun to watch. Kinda nice to have a story that wasn't like, totally soul-crushing, too. That was by far the closest thing to a happy ending we've gotten in a storymode yet.
And yes, to my knowledge, the Medicis have always had a stake in the Casino. It seems that their influence extends into nearly every single nook and cranny of New Meridian, whether that be through reputable business or underground dealings.