Science is the search for consensus about predictions. It says nothing of truth.
Science does not concern itself with "truth", it leaves that to the philosophers. Instead, it concerns itself with finding models and the (often vast) set(s) of preconditions that must hold before those models can be said to apply.
In fact, many branches of science know that they can't decide on truth, simply because of fundamental limits in what can be done by science, illustrated by things like Godel's incompleteness theorems, astrological event horizons, Heisenberg's uncertainty principle, etc. etc. etc. It's not that we don't know whether we can find truth, it's that we know that we can't, and that reality is what science works within.
And that's just for external reality. Science can't penetrate subjective experience for reasons unrelated to incompleteness, event horizons, or uncertainty principles.
I've a strong opinion that folks tend to confuse the objective and subjective by misapplying preferences or experience as "is" in far too many circumstances and too many disagreements are people attempting to dominate the objective with their personal subjective. Language, rather than helping clarify, tends to muddy the waters in these cases too.
As part of a larger project that you touched on, I believe it's important to convey the bounds of science as an epistemological process. There are other epistemological frameworks to draw on that do cover these areas and likely new ones to discover or create. If you couldn't tell, I'm an epistemological pluralist.
But this frame you've got where truth exists in some kind of metric space... it sounds like metaphysics to me.
It's the closest thing you can possibly get to a "formal truth" about the real world.
2. Science is not about belief in the ignorance of experts-- on the contrary, expertise in science is all about having the skills and the knowledge to characterize and quantify uncertainty.
When somebody announces that a certain kind of particle exists and has certain properties... And they're equipped with all of these arguments, backed by experiment, which will help you come to the same conclusion. That's science, right?
The invitation to perform the experiment, replicate the result, and start using stories about things you can't see (e.g . electrons) to explain the world around you, that's consensus building, because now you're using the same stories as everyone else who has followed the same process.
For best results we should be skeptical about any notion that those stories won't later be superceded by different ones (i.e. skeptical that they are true), but that's as much a belief in our own ignorance as it is in the belief in anyone else's. So where do the experts come in?