Well I am afraid that is putting the cart before the horse. Just because a particular theology “perfectly” fits a series of ideas doesn’t mean that theology is true. A theology can be very very internally consistent but still be wrong, no?
It is entirely possible to come up with a way in which you can have a historical Fall event involving a single couple whom all persons now living find among their ancestors. It would not, however, have been 33 patrilineal generations before David. You can have good theology whether you take the Fall as history or as parable.
I’m part of an Anglican community.