It reads to me that the stock clamp designed for a larger post ( the varsity / continental posts essentially the same as the other electro forged frames and quite small in diameter ) the nuts just run down on the clamp to get it to cinch.
Way back at Schwinn shops some saddles came with two central clamp parts for the two basic diameters of post.
Some used a collar about 340 degrees in circumference to make up the gap.
As the saddle clamp bolt most often has a square center section, trimming off the excess might work, but I have a feeling you have a basic mismatch of parts, a collar might be the best route. A local bike shop that used to sell Chicago schwinns might be a place to look.