Polynesians:

A long weekend, you say? Math time! Research says Europeans sailing ships usually did about 4-6.5 knots. 5 knots is a little shy of 6 MPH, so we'll use that as an average base. Now, take into account that Magellan's ships encountered Polynesian ships, which were noted to be easily faster and more maneuverable. so, let's say 8 MPH for an average with good wind. 8 MPH x 24 hours is 194 miles in a day, if you sail for 24 hours a day, which is unlikely since the navigator has to be awake for them to say on course, and navigators were rare enough that they could apparently hold communities hostage if there was a drought (by making them pay through the nose for evacuation or aid from other islands). Assume six hours for sleep, and let's say another two a day for hours of bad wind, no wind, or progress lost to uncooperative currents. That means a journey of 500 miles would take about four days. Seems that checks out!
But one should also account for that they would need to supply themselves with food and water as they went up and down the coasts, and anything they couldn't supply for the next six months would have to be bought out of what they get for their trade goods.

Still, overall this is definitely looking more and more plausible. Astral navigation and no reliance of charts would make them much better-suited for link usage in distance travel than most.

Library
Really, that fast? *whistle*
Okay, so they can definitely get the written language up and running. Probably properly widespread by... let's see. Chronologically, the language creation would probably have to start after they'd had a bit more peaceful contact with the europeans. Timeline says major trade with the Europeans only really began in 1600-1605. So, if we say they started on a language in about 1610, we could probably have it be widespread by 1620-25. That's 125 years to the current .
Still, though I think it may be a little much to say they would end up with one of the great libraries of the world in that time frame. It would certainly be a very large library. They could probably get ahold of a printing press, either from the fusangren or the europeans, and modify it a bit to work with their new language (which we should totally come up with some details for), then use it to start really mass-printing 'aztec bibles', a written version of the practices and beliefs already in place, approved by the priests, and educational textbooks for the schools already in place, along with a few other select books. from there, the librarians start recording everything they can and putting it in tomes in the library. Whatever history they can get from the historians, or better yet the amicqui, accounts of battle and warfare from soldiers, so on, so forth, and then they start looking for copies of books from other places, from the fusangren and the europeans, carefully translated by library priests (Who may or may not be editing selectively).

Also "It belongs in a library!" seems like a much lamer catch phrase than the original. But that does sound like a pretty awesome character.