[pbear8]

No, it is a non-publicized Mass said without a congregation but perhaps with a server.

[alternatives?]

Sorry to be a pest. So you could do it with a server and a family of four (say your parents and grandparents). The Cardinal is saying no to that.

[ebb tide]

Priests are allowed to make their private Masses available to those Catholics who happen to "drop in" to their churches/chapels for the Mass. Some priests keep their doors unlocked during those masses; some, however, lock them.

In today's climate, I really don't see any traditional priest locking the doors during a private TLM that is elsewhere unavailable to his flock.

Here's a photo of Pope Francis offering a private Mass, ad orientum: