Hmm, Star Wars. I think you're on to something with the hero idea. Something that's been lacking in CCGs in general is the concept of main hero. Teamwork is nice and all, but there's something to be said about a game that focuses on one hero. The main exception being World of Warcraft TCG. Even there, though, it's all about PvP combat.
Furthermore, when you incorporate one hero, you can add in some more complicated stuff, like multiple stats and such, because you only have one character to work off of.
What I think would be cool is the idea of a hero quest. You have a character who isn't very powerful, and they gain experience in life, honing their attributes accordingly. They gain and lose companions, until they finally achieve a Destiny. Which can vary.
I think you could easily incorporate the LOTR-ish mechanic of each player being a good guy, and having bad guy cards as well, so that good guys and bad guys alternate. So you have your hero, and he goes up against the obstacles and minions played by the bad guys.
As far as advancement goes, it shouldn't be like a game where you level-up a character. That's too MMO-grinding for me. What would be cool to see is an advancement system that alters aspects of a character through experiences. In fact, I bet that you could make that a card type. An "Experience", a card that plays to some area, and modifies the stats/abilities of your main character. This could represent minor events, skills, or even big things like mini-quests or missions that you complete.
Also, any advancement system should be story-driven and character-driven.
Lemme know if you need me to toss out some more ideas. I think this is definitely something that needs to be explored.