But there is no mechanism to share it explicitly with people you vetted. This isn't Facebook, there aren't friends with various levels of permission and a public version.

You could do that by just showing your screen to your vetted people, though, I suppose.

(a) There are friends with various levels of permission. Certain fields on the profile can be set to be visible only to certain groups of contacts.

(b) Upon noting (a), I filled out a private profile in anticipation that Google would be rolling out further mechanisms to share private profiles with certain contact groups.