Welcome to the club, the Campy GT is a boat anchor, I would put a Rally on it which can be hard to come by. They had Crane's later but I think they don't look right on these.
Interesting that it has DT shifters with the triple, maybe special order, changed or not used with the GT. This needs Schwinn branded/approved SunTour bar cons IMO.
I always carefully scrub or brass brush off the loose rust then soak with PB Blaster or WD-40 to knock the rust own as much as possible, clean/strip with brake or carb clean then soak small parts in Evaporust and clean the frame with Turtle wax rust remover and chrome polish then Quick Glo, Simichrome, etc.