Hi Olwyn,
Have you thought about buying enough wood for 20, turning 20 by hand and then picking out the best 16?
I'd suggest it'll be a lot cheaper than buying a copy attachment, a lot more satisfying and probably hardly any slower.
Your turning will also be better at the end of the process.
I remember reading about a design for a copy attachment. It was basically a rod fixed parallel to the lathe bed with a number of 'fingers' slid on to it. The fingers were just pieces of thin ply about 3-4" x 1" and they rest on the rotating work until the work reaches the correct diameter, when they drop down ( no longer being supported by the work). The fingers were of differing lengths to match up with the variations in the original piece, and there were as many fingers as needed depending on how complicated the original is.
Might be worth trying out, and could be useful for future projects.
I haven't tried it myself yet - another of those "one of these days" projects.