This creates the mistaken implication that there is some need for an affirmative belief to sum up to 100%, and I think it improperly relabels "uncertainty" as "faith."

A perfectly rational being would assign some percentage chance to evolution being true, some percentage chance to each religion's creation story being true, and some chance for any number of other theories that have not yet occurred to us. It would not feel bound to a binary, "Evolution right; creationism wrong!" that the human mind naturally gravitates to. It would be perfectly happy to think, "Evolution P=.999, Creationism P=1.2e-45" or whatever values it determined were appropriate.

Similarly, there is no red gap that needs to be bridged by faith. The only thing one truly must have faith in (and please correct me if you can; I'd love to be wrong) is induction, and if you truly lacked faith in induction, you'd literally go insane.

Rather, the religious claim of, "Well, you need to have faith to believe X" is a fundamental misunderstanding of what constitutes a proper degree of certainty. It's like the DirectTV ad where the "competitor" says, "Direct TV has 1080P. We don't. But neither we nor directTV broadcast in 1 million P! Look who just leveled the playing field!." You can "win" almost any argument by raising the bar to the certainty standard, because if it's an argument about reality, both sides will be infinitely far from meeting it. Implying that some degree of "faith" is necessary to fill the bar to 100 wrongly gives this argument credibility. The red part is occupied by likely alternatives, not by faith.

You need faith to believe that a fair coin flipped fifty times will always land heads. You do not need faith to believe that a fair coin flipped fifty times will not always land heads, even though it is possible. I think this gives a more accurate understanding of what is meant by faith.

Perhaps I misunderstand, but I think what you're calling "faith," is simply confidence level. Renaming it "faith," I think, is going to muddle the terminology more than it assists the ability to argue the point.

Let's take your view of evolution: You're saying you accept it based 1% on faith. I would say that I am 99% confident of it (assuming your view), which has the advantage that doubts that enter into the analysis would reduce my confidence level, but not increase my faith level, which would remain at zero.

Nor do I believe that this renaming helps us meet the divergent views between the faithful and the evidence-based. To give credence to faith as a necessary filler of doubt doesn't help move people toward evidence, in my view. Further, it is exactly the sort of logic the faithful cite - science is just faith in something else.

We know that heuristics “fill the gaps” in knowledge of recognizable scenarios such that we can comfortably demand less evidence and still come to a reasonable conclusion about our surroundings in most cases.

Intuition (what you call "faith") is evidence. Like any evidence, it comes with uncertainty about its implications, and dependence of its reliability on other known factors. You can't cut it some slack as a special case, rather you already know something about your mind and its heuristics that boosts the probability of them computing the right answers.

You already know that your lawful intelligence does a lot of work, considers a lot of evidence, much more than it theoretically needed, presenting its conclusions for you to feel as intuition. Even though you can't see the machinery, can't name specific pieces of evidence that drive your intuition, you know that it's there. Perhaps the greatest strength that intuitive mind gives you is ability to locate the hypotheses, something other tools just can't do.

At the same time, you know that you run on corrupted hardware, that the answers given by intuition are unreliable and may be systematically biased towards stupidity or against your values, but so are the answers of any other tool. Conditioned on the presence of features known to evoke standard biases, your intuition can be considered either more or less likely to give the correct answers. Sometimes, you have nothing except intuition and intuition is known to be compromised, but in that case you just have to acknowledge significant uncertainty in what intuition cries to be an inevitable conclusion. In other cases, you have data to update intuition's estimates to something very unlike what intuition says by itself. Often, intuition and other sources of evidence agree.

I’m not interested in more rigorous methods because I am interested in bridging the gap between the rationalist and, let’s say, those who have a propensity of demanding lower levels of evidence for beliefs.

There's no bridging this gap because the non-rationalists (e.g., honestly religious people) are ultimately uninterested in objective truth.

Rationalists can use faith in the absence of evidence, as in "taking P<>NP on faith because we haven't proved it yet". Religious people, however, use faith to believe things despite evidence that contradicts their belief.

You have no proofs for the core beliefs. They are always assumed only.

Had you have a proof for one of your core belief, it would relay on some deeper beliefs - and those were your core beliefs.

It's alway an arbitrary set of axioms you starts with. Always. An old axiom of yours can be deleted only if it confronts some others.