The Gear feat replaces the 'Not Without My Hat' forte.  No, it gives no bonuses in recovering the Hat, because Vexing Misfortune works off of the Foible and/or Story Hook: you have to have the Gear in hand for the Gear to apply..<br/><br/>Almost everything you list is covered by...well, Firearms or Athletics. If that's all you want the Forte to include, that's fine.