I think you are looking at the Trolley Problem out of context.

I understand the supposed purpose of trolley problems, but I think they're conducive to poor quality thinking none the less.

They don't offer solutions to moral questions, they highlight the problems.

Right, but I think there's better ways of going about it. I wanted to keep the post brief and information-dense so I didn't list alternative problems, but there's a number you could use based in real history. For instance, a city is about to be in lost in war, and the military commander is going through his options - do you order some men to stay behind and fight to the death to cover the retreat of the others, ask for volunteers to do it, draw lots? Try to have everyone retreat, even though you think there's a larger chance your whole force could be destroyed? If some defenders stay, does the commander lead the defensive sacrificing force himself or lead the retreat? Etc, etc.

That sort of example would include imperfect information, secondary effects, human nature, and many different options. I think trolley problems are constructed so poorly that they're conducive to poor quality thought. There's plenty of examples you could use to discuss hard choices that don't suffer from those problems.