"Perhaps a more fitting real-life analogy to the Trolley Problem would be as follows."
A non-trivial part of why the trolley problem bothers so many people is that it can't be salvaged because it is intrinsically not anything like real life. In real life you are never presented with such a binary problem. Everything is a mix of arbitrarily unbounded priorities, predictive ambiguity, and even ambiguity in the outcome.
My personal "resolution" to the problem is, yes, obviously, you save as many lives as possible even if that means actively changing the outcome... but that's essentially irrelevant, because you will never in your life be faced with such a stark, mathematically-rigid choice. There's always other options... not always relevant ones or desirable ones, but always something.
Even when you construct the problem as close to a real life one as possible, you end up with something more like "You just realized you're driving on ice and going way too fast. In front of you are two pedestrians crossing in front of you, one on each side of the road. You have about .3 seconds to consider this problem. Your System 1 instincts think you might be able to weave between them but there's a chance you'll start spinning and hit both. You could also try to jank to the right and go up on the curb, but you might crash yourself into that tree pretty hard and still hit one of the pedestrians. Regardless of what you choose System 2's gonna be second guessing you pretty hard for the rest of your life." You don't get "Choose A and this will happen, choose B and this will happen", it's a big mess. It's always a big mess.
Even if you literally encountered the trolley problem in real life, one must consider whether your understanding is accurate, or if the person who has explained it to you is lying or has ulterior motives, and so on. (And that's ignoring "this is clearly the trolley problem and I must be on TV or in a psychology experiment"; let's pretend it's in a world that isn't obsessed with this particular problem.)
Now, that is arguably the point of the trolley problem, to get down to that level and ask ethics problems. But it's dozens of layers of abstraction away from anything relevant to the real world. It's a mistake to think otherwise and stress about it as much as the gestalt seems to.