From looking at those cups, I would try a 68mm axle just to see at this point.
I agree with miamijim that it doesn't make sense that it binds, especially with cup and cone. Can you get the bearings set up right if you ignore the cups sticking out too far?
After that, I would find the best framebuilder close to you for help with this.
And not to rain on the parade, but you may be just now finding out why this frame was never built up.
Originally Posted by
Spaghetti Legs
That thickness on the SSE side is a bit of an optical illusion. It's the cable guide on the Cinelli lug, actually set back a bit from the lip of the shell. I'm fairly confident there isn't a major structural issue as the frame has a serial number (wouldn't get one right if it didn't pass QC?) and no signs of any damage or craziness done to it.