"Hidden" but still active membership types

We have Life Members of our organisation, but these are awarded to a very limited number of people rather than a membership that people can sign up for / buy.

Currently I believe a “hidden” membership more or less deactivates it regardless of the membership validity date, in that it’s hidden from the membership types listed for purchase, but also is hidden from the members that hold that membership type.

Ideally we’d like to create Life Member as a membership type that can’t be purchased, and instead we would use the Sell Cash Memberships feature to add the people that the membership is awarded to, and allow them to see that membership in their profile.