My first impression (from your description) is that, in the British context, such a series works only as a put-down, rather than a satire.
Last night on a live nature programme in torrential Scottish rain, a Welsh presenter said he’d met a man carrying planks, who said his name was Noah. My wife commented that it’s unlikely anyone under the age of 50 got the joke, and that’s true - you have only to watch University Challenge to realize that there is almost no cultural memory left of biblical matters.
Nobody here (apart from a few dinosaurs) has read a KJV for decades, nor has any idea of Ussher’s chronology… except, maybe, from scientistic programmes on evolution telling them that clowns in the olden days thought they’d pinned down the creation of the world to whatever time and date it was (whilst counting angels on the head of a pin, no doubt).
Even knowledge of the basic Genesis story is hazy (I’d say even amongst many churchgoers). So the drama seems simply to be driving home memes against what savvy people think they know of American Fundamentalism rather than satirizing any actual British religion (unless you see it as mocking a tiny minority, which would be unkind).
“Fundies will be really wild with a feminist God, that the KJV dates are wrong, that we’ve rumbled their “mock in the rock” theory of dinosaurs, and that original sin is called into doubt.” Except that there are about as many Fundamentalists like that in Britain as there are flat-earthers, so it seems to me the equivalent of a Roman TV series repeating the claim that Christians worship a crucified donkey.
Hey, but maybe it’s intended mainly for the US market, where at least you get the impression that Joe Public is vaguely acquainted with Christian teaching.