I'll definitely write a diary about quests, probably next week. I want to write one this week about where we are on our Beta progress.
If I might dissect your post: At first, I wasn't sure what to think, because I'm familiar with "replay value." That is, in game design there's an entire domain of consideration given to making sure your game IS FUN the second time. Thus, hearing you say you don't like "replay" struck me as odd. (Perhaps it's just that we've been talking about terminology too much.) But it's clear you want what the rest of us want: to have fun while playing. So I would agree that, yes, we don't need artificial ways of keeping the players playing (and presumably forking over money). But I'm pretty confident there will be no "MAKING the people replay a quest": if it's fun, the players will want do it themselves. And I think your suggestions are perfectly good for that. For the "not using a move card," what about permitting cards that, incidentally, also have a move? E.g., players could use an attack on a friend because it shoves that friend out of the way.
I think the term current exclusive title of "Quest" needs to be changed. Ether call the initial dungeons and the content that follows both quest or it's going to sound weird. In my opinion, the best method would be calling the base dungeons Campaign Quests, while everything else is just a new quest that opens up to you after beating that first quest. For extra content, each finished dungeon should have a variety of ways to play them afterwords. You will gain longevity in a number of ways. There should be a variety of odd events happening after completion, which I think was already mentioned in the podcast. Include strict settings like an all cleric party or one card per character each turn that have to be played through with the same dungeon. Perhaps it's an entirely different group you fight because the new vacancy has welcomed more devious guests. The option to replay the old dungeon at a higher difficulty or play through the default with a different fighting style and set up is a must. Maybe new quests will require you to be another 5, 10 or 50 levels higher to try out the next difficulty or to attempt some of the challenges. Some do need to be open right away to enjoy after your victory, however. Not every players wants to move on to a new dungeon immediately. One thing to keep in mind. If every dungeon area has the same type of extra content it will be boring and eventually feel like a chore to do. Increased difficulty for all of them is fine, but make sure you tailor each spot to have specific types of extra content. To finish off the topic on quests and extra content I believe what I've written isn't the end all you need to keep the players happy. Not a lot of games open up their content and let the players create what they will with it, but I think this game would benefit a lot more from having a modding community. The game already follows the heals of the largest modding games out there. I'm talking about the pen and paper phenomenon Dungeons & Dragons. I see so much that could be done if the players were given modding tools, and it doesn't kill your ability to make money proven by so many indi games released in the last year or so. Players will support, and continue to support future core development if the game is made right. >^.^<
It sounds like Quests are specific scenarios that can be seen as a "subset" of the level itself that restrict the way you play it in some way to add a variety of challenges that are not present when you just normally load up and play the given level.