I’m still trying to fuse the brilliant combat engine from D&D 4e with the brilliant narrative engine from Gumshoe. You may not have known I was trying to do this. But I am.
Let’s skip over the skills question for now and pretend that we have a Gumshoe adventure all mapped out, with the multiple paths and the clues and the major and minor scenes. It’s a flowchart, basically. None of these scenes are directly combat-related, although it may require combat to reach a given scene. Here, have a PDF example. Contains spoilers for the Esoterrorists sample adventure, though!
Now: for each scene, we may (not must) attach either a prerequisite combat, a resulting combat, or both. A prerequisite combat is a fight you need to engage in, or possibly win, in order to get to the clue scene. The clue scene might be really brief; e.g., maybe the fight happens and one of the combatants has the clue on him. Or, say, you have to fight through the kobolds to get to the secret lair in which more information is available.
A resulting combat is when they come after you for finding a clue. Actions have consequences. I think it’s important to make the linkage super-clear for the best narrative effect.
The idea is that by strongly pairing investigative scenes and combat scenes, you reduce any chance that the players will feel like they’re playing two different concurrent games with the same set of characters. This is just a theory right now. I should probably test it sometime.
Another tangential note: you could maybe keep skill challenges as long as you went with the current WotC approach, which is that failed skill challenges result in problems rather than failures. This is attractive in that skill challenges seem to be cool, but I think it’s too much of a departure from the Gumshoe skill model. Or you could ditch the Gumshoe model altogether and make clue acquisition into skill challenges? I don’t know how to run skill challenges well enough to do this, however.