I just did a check with Corsair AF quests. I was able to do the first two quests for the gun and pants. But when you trade the Hydrogauge to Leleroon, he won't give it back to you, so you have to fish another Hydrogauge in order to continue the quest.
"Against All Odds", the quest for the AF hat, does activate and you get the cutscenes, but clicking on the Cutter doesn't give you the option to enter the fight. The only option it gives you is to enter "The Black Coffin", but that's for a TOAU mission and clicking on it freezes you, forcing you to force close the game to get free.
Even with this quest activated, Leleroon in Nashmau won't talk about the last AF pieces, so you also can't get the body, hands, and shoes.
Since you're only able to get the pants at this point, this is the only piece you can upgrade to AF+1. The AF+1 pants have some nice stats but it's up to you if you want to invest in it at this point, especially since Silkworm Thread is a really rare drop in my opinion.