From what I can tell, the conclusive problems that normal utilitarianism faces are (A) the knowability problem, which is whether we could really know the total future impact of our actions, or (B) "infinitarian paralysis". These problems are sort of duals of each other in that (B) involves fixing an answer to (A) by setting the knowable limit of cardinal utility at infinity.
But so what about a version of utilitarianism where the only balance we have to deal with is the one for our present options? For example, if we kill the one person-with-healthy-organs, then at that moment by itself, the five recipients are not saved. Perhaps we might say that the killing by itself was actually wrong, but it is "atoned for" if the harvester does go on to save the five. (That might sound like gruesome reasoning, but I don't know if it's ultimately any worse, at least by normal utilitarian lights, than the mere recommendation of the harvest.)
This doesn't sound like it would solve trolley problems. But are trolley problems really solvable? If an agent is under such pressures, then based on their prior ethical beliefs, we should expect them to choose whatever they think their beliefs at least might recommend. The idea that people should spend time in their lives preparing themselves for what they might need to do if they came upon a runaway trolley and a conveniently situated other possible victim, is not practical almost at all. Granted, we might criticize utilitarianism or Kantianism (or whatever) for failing to deliver an "acceptable"/persuasive verdict in trolley cases, but I will waive that for now.
But so my question is: I have read about e.g. satisficient variants of utilitarianism that compress the maximization factor in the general direction, but are there versions of utilitarianism that have been proposed in the literature where only the immediate effects of one's actions should be evaluated, and if possible compared beforehand? Some sense of what actually counts as "immediate" would have to be developed, I realize, and maybe vagueness would creep into the picture (or potentially convoluted temporal logic), but at least the end-of-the-line default of normal utilitarianism might be avoided?
Sidebar: I don't know how to look this question up on Google directly. Bard claimed that what I am looking for is act-utilitarianism, which roughly flies in the face of everything I have ever known about act-utilitarianism. Maybe I don't know what I thought I knew, then, or maybe Bard doesn't understand my question well enough to make the relevant distinctions. I can see act-utilitarian proposals in history as having been bounded by cause-and-effect sequences with only a few relevant stages, but not compressed into one stage. For the example that most preoccupies me, if I'm not mistaken, the common utilitarian (or at least consequentialist) defense of the Hiroshima-and-Nagasaki incidents is that in a short but not immediate period of time, the attacks motivated Japan to surrender, which saved some net number of lives, etc. But since this happened in multiple stages, even if in a few days, yet since it involved two air raids that were already separated in time, this kind of argument wouldn't be licensed by the version of utilitarianism I'm asking about.