Re: the improbably longevity of the Maesters, is it possible that the sources are simply… unreliable? I mean, it wouldn’t be the first time an institution claims to be more venerable than it really is.

Is possible that there were no maesters before the Andal invasion, and they’re just inventing their pre-Andal history to increase their status? There are stories in Westeros about “knights” who are thousands of years too old to be knights.

That would be the simplest, rational answer. Except that, as we’ve seen in ASOIAF, the simplest rational answers that the modern maesters insist are the truth are wrong. Most maesters insist that ravens cannot speak and consider Barth a quack, but we’ve seen Bran talking to Stannis through them; Maester Fomas argues that:

“the Others of legend were nothing more than a tribe of the First Men, ancestors of the wildlings, that had established itself in the far north. Because of the Long Night, these early wildlings were then pressured to begin a wave of conquests to the south. That they became monstrous in the tales told thereafter, according to Fomas, reflects the desire of the Night’s Watch and the Starks to give themselves a more heroic identity as saviors of mankind, and not merely the beneficiaries of a struggle over dominion.”

But we’ve seen the White Walkers in the flesh. Maesters believe that “the higher mysteries, the arts of magic, were and are beyond the boundaries of our mortal ability to examine,” but with Bran, Melisandre, Dany, etc. etc. we have seen that the higher mysteries are quite real and achievable.