I agree that there should be some sort of card duration extension, but I don't think it should be mashable.
As for your suggestion about cards working differently on different roles, I think it would improve things in that you would be able to choose between damage mitigation, healing power, and dps, but part of me rankles against it because it would completely do away with the rng component of the class (which has also been removed under the current system). What I loved about AST was working out how to make the best of whatever hand you drew. And yes, that had problems for reliability. Also, your system would still limit your choices more than I'd like, since you wouldn't be able to put some mitigation on the dumb dps who keeps standing in stuff. Or restore some mana to the magical dps that just got rezzed. So, some suggestions of my own (quite possibly which have been written elsewhere by other people but if they have I don't remember who or where):
Keep the current lord/lady system but revert the original cards (in effect if not in potency, and putting something new on spire). Now every card can be a damage buff. No useless cards
Force the fates (cooldown): allows you to forcibly draw a card of your choice (would temporarily change your basic moves into card icons for selection much like the dancer steps). Now you can have reliable mana restoration or damage mitigation as its needed, and if you feel comfortable without that assurance you can burn it for more damage instead.
Bag randomisation (there's a thread for this one): ensures that you won't draw the same card over and over by picking from the cards you haven't already drawn until you've drawn all 6 is sequence. This, along with:
Shuffle (cooldown): resets the bag randomisation, so if you just got all the cards you want in a row you can have a chance at drawing them again without having to draw the ones you didn't want first.
I know some people will say that we should be focusing on how we can fix the new cards because there's no going back, but... to be quite honest I don't think there's any salvaging the new cards. Unless they actually differentiate between the effects of each card. At which point they might as well go back. And I know there are some people who like the new system, but clearly a lot of people don't, and I will continue to push for change because the only two classes in this game I really loved (SCH and AST) are currently in a place I can't bring myself to play them any more.