If you go too far one way, like towards LastFootnote's system, you'll knock out the most objectionable cards, which can at some point include the best options.
Wait, what? How does this make any kind of sense? Could you give an example of how this could happen?
I'm trying to follow your train of logic. How is it that the most 'objectionable' cards can include the 'best options'? If people think a card is objectionable, they won't vote for it. If they think a card is one of the best options, they will vote for it. If what you mean is that the cards that people vote for aren't actually the best options, then no sensible democratic voting system is going to give you what you're looking for.
If what you're worried about is that everyone will vote for not only the interesting cards they like, but also all the boring cards that they see as 'good enough', then that's a problem with the voters themselves. However, I don't think we have to worry about this, because I think most people will find boring cards 'objectionable' and will therefore not vote for them. If people genuinely like the 'boring' cards, then who are we to argue?