We Should Not Accept Scientific Results That Have Not Been Repeated

No it's very simple. If you want "the people" to pay for you to do things at all, you owe them all of the things or you don't get their money. Your objections make it seem complicated but this feels like an effort to muddy fairly clear waters.

We shouldn't "accept" or "reject" results at all.

It's not a binary option. One poor experiment might give us some evidence something is true. A single well reviewed experiment gives us more confidence. Repeating the results similarly does. As does the reputation of the person conducting the experiment and the way in which it was conducted.

It's not a binary thing where we decide something is accepted or rejected, we gather evidence and treat it accordingly.

Thinking about physics, the LHC experiment benefits from not being a completely isolated study. Instead, its results are multiple pieces of a larger jigsaw puzzle or web of interconnected results that include both a quantitative predictive theory and other experiments that test other predictions of the same theory. And the Higgs was not the only thing that could be tested at the LHC. For instance, it probably replicated a huge slew of prior studies during construction and testing of the system, from already-known particles all the way down to the calibration of voltmeters.

In physics, some theories have been tested and interconnected to such a degree, that if an experiment conflicts with theory, it's reasonable to suspect the experiment rather than discard the theory. That's what happened with that apparent faster-than-light travel of neutrinos captured in Italy. It was something like a partially unplugged cable. Once corrections were made for the cable, the theory snapped right back into place. Those theories can be trusted as akin to tools in day to day physics. For my humble graduate experiment, refutation of any major law would have led me to fix the experiment and try again. I simply assumed things like conservation of charge. Such laws probably include electrodynamics, gravitation, quantum mechanics, thermodynamics, and Darwinian evolution.

And this is a common feature of major studies in physics, chemistry, evolutionary biology, and other sciences as well.

Where we may run into trouble is in branches of sciences that don't have over-arching theories or that web of connected results. At the other end of the scale are areas of sciences where the results are mainly a database of observed statistical correlations, with little or no apparent progress towards a general theory. When someone publishes a surprising result, there is no reason to say that the experiment must have been done wrong. You just add it to the pile. The best that can be hoped for is that some kind of meta-analysis will demonstrate an inconsistency among multiple studies. Those fields don't have the "hard" theories that can be used as tools to test experimental results.

To be fair, there's another situation, where you have not one, but zero, reproducible results. That's the state of affairs in the search to unify gravity and quantum mechanics.

"I don't think reproducibility should necessarily mean literally repeating the same study over again."

Yes, it should. We have too many demonstrated instances of studies built on other studies that turned out to be flawed, but the second study, rather than showing the first one was flawed, was rationalized and massaged until it conformed to the first study because the first study already had the imprimatur of peer-reviewed correctness on it.

Only someone replicating the original study directly (give or take sample size or duration or other simple such changes) will have the guts and moral authority to stand up and say "I can't replicate this. The original study may be wrong."

The entire post-war research system is set up to create endless streams of non-replicable studies based on incorrectly-applied statistics all the while convincing itself that it's doing something useful while wasting billions upon billions of dollars.

I'm not to impressed by "well, that's not how it works right now". The whole problem is "how it works right now". That's what we're discussing, the need for it to not work that way.