The Shimano/Campagnolo discrepancy shouldn't result in play in the bearings; something else is responsible for that. Is it perhaps a spindle designed for a 68mm shell being used in a 70mm wide shell? That might make it difficult to adjust without bottoming the adjustable cup in the shell. Or is it the arm loose on the spindle causing the play? Check for damage in the square bore of the crank arm.

Re: C-Record bottom bracket compatibility with vintage Super Record cranks. I've not tried it, but my suspicion is that it won't work. The C-Record spindle is symmetrical, while the vintage Record spindle is asymmetrical. Nor are the internal parts interchangeable: C-Record uses 3/16" balls, while Record uses 1/4" balls.