Brandon:
The oversized sway bar like looking parts you describe are simply bolts and cushions to attach the leaf to the trailing arms. You can obtain them from any major vendor of Corvette parts.
What you might try is going on line to Vette Brakes and Products, Zip Corvete Parts, Long Island Corvette Supply, Paragon, Mid America Corvette or any other Corvette parts supplier. They all have them.
For your differential parts try Bair's Corvette Parts or once again Zip, Paragon, etc.
This stuff isn't that difficult to obtain.
You posted that you haven't worked on a C2 before. Either you or the owner of the car should obtain a service manual so you won't be blind on what you are doing. It is just as easy to screw up one of these cars as it is to repair it properly. Don't be that guy that screws it up because of a $50 dollar or less expenditure for the manual.
Rich