> I haven't read The God Delusion or wherever the "god of the gaps" critique originated - what is this actually referring to?
A rare point of agreement between Nietzsche and the evangelist Henry Drummond was that the Christian apologetic approach of "ah, but that hasn't been explained yet, so it must be God's will" to all the discoveries of the Enlightenment wasn't a very impressive one. Not least because of the tendency of gaps to cease to be gaps.
Ultimately "the more we learn, they more we learn we don't know", to quote the OP is a route to agnosticism not a belief in a particular deity, and it's particularly hard to see an omipotent, benevolent God who created man in his own image in the incomprehensibility of quantum indeterminacy to the average layman (although I'll give credit to the creativity of those suggesting that three quarks must be proof of the Trinity)
> What serious Christian or Buddhist thinkers using religion to explain things like weather or medicine are being referred to here?
It'd be easier to ask what serious theologian said "nope, this stuff about the weather being controlled by divine fiat and pestilence being a punishment for the Fall is just stories and actually you might be able to alter them - perhaps even in your favour - as soon as you stop praying and start doing." well in advance of the accompanying science? Augustine, since you're apparently a fan, was pretty confident that the problem of pestilence was the product of a literally occurring Fall involving two actual First People, which doesn't square very well with evolutionary biology.
Monotheism hasn't quite had the problem of people landing on the moon god, but it's fair to say that what many mainstream monotheists believe today has changed considerably in scope from what mainstream monotheism purported to explain for most of its existence.
> As early as St. Augustine, writing around ~400, and one of the most influential Christian thinkers, we have discussion of the account of creation in Genesis being metaphorical
Sure, Augustine made four different attempts to explain Genesis because even in his time the six day account - still an article of faith for many other Christians even today - didn't make much sense. None of them involved evolution from apes, and he still ended up with Adam and Eve being literal people who caused suffering for everyone [and everything] else via Original Sin.