My favorite answer is that you should act to preserve as many lives as possible as long as you don't reduce another human being to a mere means to an end.

Normal trolley problem: Switch to the one person. You aren't "using" the person, the solution works regardless of whether the person is tied to the tracks. It's just unfortunate that the person is there.

Surgery analogy (is it okay to kill one person and harvest their organs in order to save five): No because you're taking that person's life in order to go ahead with your plan.

With the fat person example, I'd say you shouldn't push the fat man.

The MASH example is different from all of the above because it lacks perfect information. Pulling the lever doesn't sometimes fail. The trolley doesn't sometimes come to a peaceful stop. The baby might keep quiet. That makes it a much more difficult situation - but, due to the imperfect information, it's also not a question that lends itself to being "solved".

Personally, I don't know what I would do. If a hundred lives were at stake I hope I'd have the strength to kill the infant. If only there were only ~5 and the infant made a sound only once in the past 24 hours, maybe I do nothing and hope for the best.