I am not so sure that we can say that galaxies with redshifts z>14 are actually "exceedingly rare" at this point. Considering the tiny angle of view by Webb to see them, and the long time that it takes to acquire sufficient light to be detectable, it seems that there must be a pretty significant number of them. And, we really are not resolving them well enough to understand their detailed structure.
Anyway, if we want to really know how many there are and how long ago galaxies really did form, we are going to have to find a way to actually look, because, as you say, the theories are constantly needing revisions whenever we look farther into space and back in time.
And, remember, the actual cause of the CMBR is still only a theory, at this point. Wouldn't you be surprised if it turns our to be something else, and whatever perturbations are in it are not really relevant to galaxy formation at all?
As you say, we don't understand "dark matter" at all. Some people are looking for it to "decay" and provide use with evidence in the electromagnetic energy domain that we can detect. What if it does decay and that emits microwaves? (Not saying that it does, just pointing our how little we really know for sure.)
We are probably going to have to stop thinking that our theories are facts if we really want to advance our understanding.
Webb is already telling us we will need a bigger telescope.