I've been kicking around an idea for card-based play in Cults Across America for a long time, and what with these new-fangled forums and all, I thought I'd throw the basic idea out there for commentary. It bears noting that Source Poobah Bob Brynildson originally suggested that CAA should have something like this.
The idea, basically, is to use a Memoir '44 style card-based system for governing who gets to move their cultists, and when. Rather than going around the table and taking really long, laborious turns where you move all of your counters (which also means that you sit around for a really long time doing nothing between your turns), your turn would consist of playing a card that lets you move (say) a half-dozen counters (and their equipment) in some particular region of the board (the Pacific Northwest, say). Then, you can fight with those counters if you want, and then it's the next player's turn to do the same. Play proceeds around the table a lot faster, because each turn you only deal with a small subset of your available forces.
Obviously, this would entail either a new deck of cards or a large addition to the basic deck, but other than that, I think this would be a cool new direction for the game.
Cults is a great game and a faster game would be even better. We always play with the limited number of turns based on the number of players. This narrows the time down and we always finish games that we start. Having said this, games are still long. On a certain level we actually like long games because every involved knows this and one game of Cults can be an entire night of hanging out.
It's been a while since I've played, but my group of friends has a trick for speeding up game play. I'll talk with some of my friends and get back to you on that.
One of the great things about Cults is that the game is incredibly simple. My friends have often played it with people who don't normally play board games or RPG's. They understand the principles having played Risk, or any other board game, but the topic and rules make this so much more entertaining than a 'regular' board game. I point this out because I'm not familiar with a 'Memoir 44" system and I wouldn't want the introduction of a card based system to scare off people who don't make a habit of playing games. That is if it sped things up, but at the expense of accessiblity- then I wouldn't want it.