Just wanna point out that it's explicitly stated that Carvallain's boat has a clandestine Ceruleum engine. He didn't use it until after the Sirensong Sea, at least to the knowledge of the player, but Alisaie sure as heck figured out it was there and questioned the fuck outta that dandy boy about it.

Realistically if you wanted to conserve fuel, but get where you're going quick, then you could use the Ceruleum engine when the wind was against you or wasn't with you. I have no idea if the sea around Thavnair has still winds except in/right after the monsoon season in India, but the Sirensong Sea was what, somewhat around that point but a bit southy south?

In the real world it took a European sailing ship about a full year to reach the Dutch East Indies, what with sailing around the horn of Africa and all, and then hitting the still winds in the Indian Ocean. We've no Africa analogue in FFXIV, so we can take out 6 months there, assume Ceruleum engine use for half the trip... and I'd say that gets the trip for our WoL down to about 2~3 months.

As for why we didn't just hop on Cid's Excelsior... other than it wasn't in the script... well there's the fuel reason. Then I guess the fact that it's all imperial territory, and they have almost nothing but airships, whereas their naval power is mistakenly on their part, absurdly weak. Stupid Garleans, having weaknesses that are hella convenient for the plot.