Wouldn't you say the closest thing would be the Adamantite Barbuts (Craftable i180 gear). It's what Faye wears.

I have been looking for a cowl-esque headpiece too.

I've been trying to make a Final Fantasy Tactics Knight's Templar glamour for a long time. They wear hoods/cowls over their plate mail.

Isn't the Library's Fending headpiece just Spectacles or something?