Received the replacement parts. The handlebar was identical and the bike side of the stem was too, but the aluminum clamp for the front of the stem was a little different.



I think the original ones may have had some grooves, but they could not have been as deep as in the replacement - the original clamp was worn, but not that much. The thing is, although this clamp has some grooves they are not the same spacing as the shallow splines on the handlebars, which are much closer together. In other words, the grooves don't fit into the splines to lock the position of the handlebar, one can rotate the clamp pressed on the handlebar and not even feel much of a clicking as one set of ridges passes over the other.

Anyway, we tried bolting the replacement on and it could still be wobbled up and down slightly when maximally tightened. So we took the new parts to a local bike shop and the fellow there whipped out his calipers and said that the handlebar diameter was 25.4, but the clamp diameter was bigger, around 26.0. He had some stainless steel shims for a 25.4 to 26.0 fit (the shop sells a lot of Italian bikes) and we took them home and reassembled using those. That seems to have helped, I cannot feel the handlebars moving relative to the stem now, when pressure is applied vertically on one side or the other, and before I could.