On point number 3, speaking of theologically diverse, I think it is worth looking at how the Catholic Church has handled the issue of science and faith in modern times.
I think the more “Bible only” Protestant churches see conventional science and cosmology and especially evolution as an attack on the authority of the Bible. And they have no authority other than reading the Bible in a very literalistic way, which to them is the only safe way to read the Bible. I think this is why Young Earth Creationism is so common in America, and not just in churches that are strictly fundamentalist. I have found when talking with people that this is a brick wall - “You don’t believe the Bible.” “You don’t know the Bible.” Of course the task would be reaching people who are questioning and open minded, like a student who hopes there is more than YEC and atheism.
“Life is what happens to you while you are making other plans”.
It may wind up being the same on your second list, but since you ask…
Regarding number one, if what you are talking about is the framework in which we seek answers then I agree. For example we should dialogue on the basis of reason, in an honest manner, and treat each other with respect when this is done. I am “down for the struggle” with that. If it is a unity on specific answers to the question, well drives for “unity” of position have ever been the bane of truth discovery.
Number two is a given in that it is most reflective of who you are. This comes through even while you stay “agnostic” on specific answers. I endorse it fully.
I don’t think you can stick with number three. You are bringing the two-population model to the fore, and it is one of the distinctives here and will be regardless of whether you adopt some formal rule of “neutrality” or not. That that it should be a requirement or anything, but it is a distinctive that you are offering to the debate on theology and science. And the church needs that whether they recognize it now or not because its what the text says and its what the record of nature allows.
BioLogos is “theologically neutral” and it winds up just being a place to try and browbeat Christians to believe evolution occurred while shying away from theological content. I think the openness should be more out of an effort to have, on non-essential issues, the “educated mind” of Aristotle who said such a mind was marked by the ability to entertain ideas with which one did not agree. This dovetails into a call for a return to theology returning to its roots as a type of science, distinct from natural science, but using similar methods on different subject matter.
I don’t feel much qualified to comment on number four.
In that they don’t care about theology. They don’t even particularly want theology. They just want to convince Christians that macro-evolution is true. They don’t want Adam or Jesus getting in the way of that mission. That’s how I see it. If by “Theologically Neutral” you mean like BioLogos, then I am against it. If I wanted that I’d be at BioLogos, not here.
That is my personal experience from my time attempting to participate there. They may have something on paper. In practice attempts to steer the topic towards Christian theology, unless it directly related to getting Christians to accept human evolution, were treated with some disdain by the moderators and buffeted by the atheists which dominate that board.
A starting place is affirming central Christian beliefs - obviously Christ’s birth, death, and resurrection. I don’t know how much detail is needed. Without the extreme of going into the weeds about denomination-specific issues such as predestination vs. free will, the proper mode of baptism, etc. I think people who were raised in fundamentalism in particular are afraid that once you get rid of a literal 24 hour per day creation week in Genesis you are just a few steps away from doing away with a literal Jesus. That is not an unreasonable concern given where they are coming from.
The Catholic Church has plenty of problems, some really horrible problems (I say that out of sorrow, not out of smugness). They don’t have a strong YEC movement. Even very conservative Catholics tend not to have as much as a conflict about science vs. faith - not that I have seen.
I used to think that way about Catholics, but then I became aware of subgroups. some of which are skeptical about evolution (e.g. Fr. Michael Chaberek), or other scientific claims - including special relativity and helio vs. geocentrism. It is somewhat true, though, that in my experience these groups sound philosophically more sophisticated than common caricatures of the “Bible-only” YEC fundamentalists. Perhaps because Catholics are in general less against drawing from prior philosophical and theological traditions.