Ok, Wayne. I got the envelope a few minutes ago and took pictures. Sorry I can't get my camera to work well on close up detail of the wire, but here's what I've got for you...
The wire you provided and the wire I purchased look and feel identical. No size difference that I can tell.
While taking the pictures, I figured a person could easily save a buncha bux if they have a couple simple wood handles, use a table saw to cut a center groove, and then merely wrap wire and tie tight. You just have to redo the wire every few cheese wheels, but that wire must be $2 for lots of length, so you could have dozens of these across the years for less than the price of 12 plastic ones from a store.