In any case, I think you've just got to practice by incorporating that intuitive process into your life more.
Thanks for the thoughts, everyone. Benjammin, I was thinking that the answer would probably be what you suggested. When you're faced with a situation where you don't have some loose framework to guide your priorities and actions (like the ABC's, using the first aid metaphor) or a specific procedure in mind (like splinting a forearm fracture), and you're faced with a novel situation or set of circumstances where you don't already know what the "right" course of action should be, that's something difficult to try and mentally prepare for.
I'll have to figure out some kind of mental game to get me trained to be mindful of trying to think of a next step because just trying to regularly think of random things that could theoretically happen while I'm going about my life is rather difficult. I'll probably need to key off some action that I observe, then do the what-if? kind of game.
I think I do that already driving, but the possibilities are mostly just driving related possibilities--"What if that car on the corner pulls out suddenly in front of me? That car in the lane next to mine up ahead seems to be weaving a bit--maybe DUI or maybe just distracted so maybe I should move over another lane. The light is changing and that car approaching from the side is still going awfully fast--better not go right when my light turns green because they might run the red." I'll need to try and broaden the situations where I actively do that kind of thinking.