Utilitarianism sometimes supports weird things: killing lone backpackers for their organs, sacrificing all world's happiness to one utility monster, creating zillions of humans living on near-subsistence level to maximize total utility, or killing all but a bunch of them to maximize average utility. Also, it supports gay rights, and has been supporting them since 1785, when saying that there's nothing wrong in having gay sex was pretty much in the same category as saying that there's nothing wrong in killing backpackers. This makes one wonder: if despite all the disgust towards them few centuries ago, gay rights have been inside the humanity's coherent extrapolated volition all along, then perhaps our descendants will eventually come to the conclusion that killing the backpacker has been the right choice all along, and only those bullet-biting extremists of our time were getting it right. As a matter of fact, as a friend of mine pointed out, you don't even need to fast forward few centuries - there are or were already ethical systems actually in use in some cultures (e.g. bushido in pre-Meiji restoration Japan) that are obsessed with honor and survivor's guilt. They would approve of killing the backpacker or letting them kill themselves - this being an honorable death, and living while letting five other people to die being dishonorable - on non-utilitarian grounds, and actually alieve that this is the right choice. Perhaps they were right all along, and the Western civilization bulldozed through them effectively destroying such culture not because of superior (non-utilitarian) ethics but for any other reason things happened in history. In this case there's no need in trying to fix utilitarianism, lest it suggest killing backpackers, because it's not broken - we are - and out descendants will figure that out. In physics we've seen this, when an elegant low-Kolmogorov-complexity model predicted that weird things happens on a subatomic level, and we've built huge particle accelerators just to confirm - yep, that's exactly what happens, in spite of all your intuitions. Perhaps smashing utilitarianism with high energy problems only breaks our intuitions, while utilitarianism is just fine.
But let's talk about relativity. In 1916 Karl Schwarzschild solved the newly discovered Einstein field equations and thus predicted the black holes. It was thought as a mere curiosity and perhaps GIGO at the time, until in 1960s people realized that yes, contra all intuitions, this is in fact a thing. But here's the thing: they were actually first predicted by John Michell in 1783. You can easily check it: if you substitute the speed of light to the classical formula for escape velocity, you'll get the Schwarzschild radius. Michell actually knew the radius and mass of the Sun, as well as the gravitational constant precisely enough to get the order of magnitude and the first digit right when providing an example of such object. If we somehow never discovered general relativity, but managed to build good enough telescopes to observe the stars orbiting the emptiness that we now call Sagittarius A*, if would be very tempting to say: "See? We predicted this centuries ago, and however crazy it seemed, we now know it's true. That's what happens when you stick to the robust theories, shut up, and calculate - you stay centuries ahead of the curve."
We now know that Newtonian mechanics aren't true, although they're close to truth when you plug in non-astronomical numbers (and even some astronomical). A star 500 times size and the same density as the Sun, however, is very much astronomical. It is only sheer coincidence that in this exact formula relativistic terms work exactly in the way to give the same solution for the escape velocity as the classical mechanics do. It would be enough for Michell to imagine that his dark star rotates - a thing that Newtonian mechanics say doesn't matter, although it does - to change the category of this prediction from "miraculously correct" to "expectedly incorrect". It doesn't mean that Newtonian mechanics weren't a breakthrough, better than any single theory existing at the time. But it does mean that it would be premature to people in pre-relativity era to invest into building a starship designed to go ten times the speed of light even if they could - although that's where "shut up and calculate" could lead them.
And that's where I think we are with utilitarianism. It's very good. It's more or less reliably better than anything else. And it managed to make ethical predictions so far fetched (funny enough, about as far fetched as the prediction of dark stars) that it's tempting to conclude that the only reason why it keeps making crazy predictions is that we haven't yet realized they're not crazy. But we live in the world where Sagittarius A* was discovered, and general relativity wasn't. The actual 42-ish ethical system will probably converge to utilitarianism when you plug in non-extreme numbers (small numbers of people, non-permanent risks and gains, non-taboo topics). But just because it converged to utilitarianism on one taboo (at the time) topic, and made utilitarianism stay centuries ahead of the moral curve, doesn't mean it will do the same for others.
What about all the angst people had over things like irrational numbers ,infinitesimals, non-smooth functions, infinite cardinalities, non-euclidian geometries?
I think what you're saying about needing some way to change our minds is a good point though. And I certainly wouldn't say that every single object-level belief I hold is more secure than every meta belief. I'll even grant you that for certain decisions, like how to set public health policy, some sort of QALY-based shut up and calculate approach is the right way to go.
But I don't think that's the way to change our minds about something like how we deal with homosexuality, either on a descriptive or a normative level. Nobody read Bentham and said, "you know what guys I don't think being gay actually costs any utils! I guess it's fine". And if they did, it would have been bad moral epistemology. If you put yourself in the mind of an average Victorian, "don't be gay" sits very securely in your web of belief. It's bolstered by what you think about virtue, religion, deontology, and even health. And what you think about those things is more or less consistent with and confirmed by what you think about everything else. It's like moral-epistemic page rank. The "don't be gay" node has strongly weighted edges from the strongest cluster of nodes in your belief system. And they all point at each other. Compared to those nodes, meta level stuff like utilitarianism is in a distant and unimportant backwater region of the graph. If anything an arrow from utilitarianism to "being gay is ok" looks to you like a reason not to take utilitarianism too seriously. In order for you to change your mind about homosexuality, you need to change your mind about everything. You need to move all that moral pagerank to totally different regions of the graph. And picking a meta theory to rule them all and assigning it a massive weight seems like a crazy reckless way to do that. If you're doing that you're basically saying you prioritize meta-ethical consistency over all the object level things that you actually care about. It seems to me the only sane way to update is to slowly alter the object level stuff as you learn new facts, or discover inconsistencies in what you value, and try to maintain as much reflective consistency as you can while you do it.
PS. I guess I kind of made it sound like I believe the Whig theory of moral history, where modern western values are clearly true scion of Victorian values, and if we could just tell them what we know and walk them though the arguments we could convince the Victorians that we were right, even by their own standards. I'm undecided on that and I'll admit it might be the case that we just fundamentally disagree on values, and that "moral progress" is a random walk. Or not. Or it's a mix. I have no idea.