To play devil's advocate about the boat trips, Carvallain has a ceruleum engine on his ship.

This, in essence, makes it similar to a modern day sailing ship in terms of travel time.

The average speed of a modern merchant ship is anywhere from 12 to 20 knots, and we're talking the big honkin' metal ships. Carvallain's is made of wood. Without the engine and just the sails, it should travel roughly 4 to 5 knots.

A speed of 4 to 5 knots gets you about 120 miles a day(193 KM).

We can't actually fill in the variables we don't know. Like, how strong is Carvallain's ship's engine? How many malms are between Limsa Lominsa and Kugane? What is the wing flapping velocity of an unladen colibri? But we can do some real world analogues to see if our, "it took several months theory" holds up.

First we'll average the lowest speeds Carvallain's ship could go at, and put it at averaging 8 knots. I don't think it's unreasonable to assume that he turned the engine on when the wind was against the ship.

Next we'll take a real world distance. The UK to Japan is 4172 Nautical Miles. At a speed of 8 knots it would take a ship roughly 21.73 days to get there. You might think, "Hey, the crew has to sleep!" But ships don't stop just because the crew does. And crews on ships rotate, so ships travel constantly throughout the night and day.

This means it's actually less than a month and a half to go from Limsa to Kugane, assuming they're similarly far apart as the UK and Japan. Which honestly, nothing in FFXIV has given me reason to think that they'd be further, but for arguments sake, let's say they were twice as far apart as the UK and Japan.

A one way trip then, at 8 knots, takes 43.46 days. So anyway you slice it, it really didn't take that long.