Otto, I think you meant 5/16" bolts, which have a 1/2" hex head. 1/4" bolts or even #10 screws would be plenty to hold them in place.
Another possible source for original style clips is Restoration Specialties. They have a ton of different style similar clips.
LINKOr you could use the plastic "Christmas tree" style push on fasteners. Or split rivets if you want to stay with steel.