Insert a 1/4 20 Threaded rod into a threaded 21/64 hole through metal
Let me take another swing at this.  

This is a common issue when hanging pipe or conduit: your threaded rod goes up, but you need adjustability.  Preferably without having to take it all apart. 

I would use a basic pipe strap. 



Cut it so there are an odd number of (major) holes. Make a loop. Then use a short 1/4-20 screw to go through first a washer, then both outer holes (creating a loop around the screw head), then on into the concrete fastener.   Now a loop of pipe strap dangles from the fastener.  Run the threaded rod up through the center (bottom) hole, then a washer, then a nut. It will stretch out vertically, but you can turn the nut to adjust height. 



First, that binder isn't made for .328 rod.  It is made for solid 1/4 to 5/16 rod, exactly like it says on the tin. 



Now, using the setscrew hole is not a great plan.  It's the wrong size and pitch (finethread), and you won't find an adapter from 1/4-20NC to 5/16-24NF (if it's even that), not even a helicoil.  

Also, the fastener only pivots 15 degrees from straight, but even if that is acceptable, it's not made to have tension loads through the ball joint, it's designed for shear loads across the ball joint. 

However I would also consider standoffs like these if you can find them in 1/4-20.