I like both of your ideas, actually.
Episodic stories could indeed allow them to incorporate new DLC characters and stages naturally. Maybe these chapters could come after a certain DLC wave so that it almost mimics how they used to release Super versions of the main game. Cliffhanger abuse would indeed be a possible problem with this, but maybe there are ways to avoid that and still keep the episodic story going.
Your other idea sounds even cooler potentially. The idea that the story mode, special rival battles in particular I'd say, could be player driven and not just AI driven seems quite revolutionary and it would fit perfectly with the modern trend of the player's playing experience mattering and of personal player stories being an integral part of the game's story (like in open world games).
The idea that other players, ala that one Demon's Souls
, would take up the role of a rival during a story battle when they, for instance, are already in a special lobby playing as that character (or when their statistics show that they often play as him/her) seems interesting. It would make each battle feel more meaningful, though a possible risk is that you could get stuck in the game because of being matched with a very touch rival (unless they also find a way to keep skill in mind with this system, like you mention as well I believe).
With the announcement of that Capcom Fighters Network service to help people keep track of all kinds of statistics, improve their skills and turn everyone into a competitor on a shared world stage, and Capcom's apparent commitment to make SFV a dynamic, more story driven game that will get lots of new content over time, making the story mode (and other modes) in such a way that the story can adapt to new content and your own playing style, and also in such a way that the usual hard line between offline and online can be softened, seems like a interesting approach indeed.