That's one of the reasons why I want this game to have a variety of story types that it can tell. It's always going to be focused around combat with rubber swords and other padded weaponry, that's what lures the players in and that's what they expect to find, so it would be a nasty bait-and-switch to make the game focused around something else.
A story in this game needs to have a variety of scenes, and each of those scenes should have a variety of opportunities for different types of characters to succeed. Perhaps a bit like the current crop of scenario driven miniature battlegames, where everyone plays the games to win, and the predominate method to win a scenario is to eliminate an opposing team, but scenarios may allow a team to earn victory points by capturing objectives, gathering resources, holding ground, or something else important to this particular moment in time.
In a miniature battlegame, you choose your team then you often randomly determine a scenario so that you can't min-max your team to specifically handle it...instead you need to create a balanced team that could handle a variety of potential situations. You might have a regular set of tactics with the team you've designed, and every team will have specific strengths (that favour certain paths of play) and weaknesses (that hinder other paths of play). A part of the luck in the game comes from hoping for a random scenario that hinders your opponent more than yourself.
In much the same way, when someone offers to GM a story for you, you hope that your character will be playing to their strengths. This basically works in game, because your character would have a higher likelihood of choosing to engage in missions where they'll play to their strengths, but not all scenes will be their forte, they'll do best if they pick a group of allies who are able to handle a variety of scene types.
If we work on the assumption that a game day will be divided into 4-hour morning and afternoon sessions, or perhaps even multiple 3-hour sessions like a convention, we might work on the further assumption that a typical scene takes a 1/2-hour to resolve. Using these assumptions, a story might consist of 6 to 8 scenes. Combat scenes aren't like in a tabletop game, they don't take an hour to resolve a few minutes of melee, instead they play out in real time. Combat scenes can be exhausting, especially long ones...so while a tabletop game can devolve into a slugfest of die rolls, a LARP conflict doesn't commonly suffer from this, but a strategically interesting conflict might drag on (or at least reach a tactical stalemate).
I don't know that I'm explaining this well.
My main point here is that a story should change things up, rather than simply be a string of fight scenes. Perhaps a briefing scene, then an infiltration (which might lead to a fight if it fails), followed by a search, then solving a puzzle from the objects found, then an escape (which might lead to a fight again if things get complicated), a secretive travel (or chase scene) across town, then a meeting with the original hiring character to negotiate the transfer of information or found item.
Scope for foghting, scope for other ways to accomplish the hiring character's task.
I'm thinking of a quick way to generate stories according to a series of templates or formula, perhaps even using the Hold 'Em Scene Generator system (which you can find over on RPGNow).
Still more thinking to do.