Are there are any rules that cover using stances in story mode? Everything I've read only covers their use in encounters.

Since there are no turns in story mode, it follows that a character wouldn't need to expend time or stress to go straight to the farthest end of his reckless/conservative spectrum. Since stance dice are superior overall to characteristic dice (as stated in the rulebook itself), it would certainly behoove players to be at one extreme or the other.

So, anything in the RAW on this?

By RAW you don't get to convert any dice to stance dice in story mode (although I think NPCs always use their default stance). The GM may allow it if he thinks it's motivated (by roleplaying or otherwise). I almost never allow my players any stance dice in story mode.

As you point out, the chance of success is a lot higher with stance dice, so if the GM wants to allow stances in story mode he probably need to use harder checks to provide a challenge.

Stance dice in story mode present a few problems because the 'price' of stance (delay and exertion) does not always hold up. Sometimes delays and exertions are irrelevant if there is no pending action or time constraint. This can be worked around with a little creativity though. I wouldn't allow stance dice in story mode unless I was prepared to assign appropriate and relevant penalties from a delay or exertion.

Let's say the players have found a locked box, they take it back to town and that evening the thief tries to pick the lock. If she uses reckless stance and gets exertion, so what? She's gonna go to bed right after. Granted there are banes on reckless dice as well, but what about conservative? What does a delay mean, when she's got all weekend to unlock the thing before they need to catch a boat to Marienburg?

If you have house-rules regarding long-term fatigue and stress, then reckless stance may be okay. For the delay, you might rule that if she takes all weekend before pulling it off, so she can't get anything else done.

I allow this sometimes, but you've just got to keep an eye on the ramifications of the exertions and delays.

I allow the players to more 1 step into a stance when in story mode. I require them to roleplay it, especially if they want to use their "secondary" stance.