I don't want to get into the old debate about the mode of production, mainly because I think that's unresolvable. I don't really think the 19th Century conceptualisation is as central to historical materialism as some would have us believe. I think (e.g.) De Ste Croix's idea of (if you like) a "mode of surplus extraction" is useful (and not exclusive of mode of production).
"Primitive Communism is ... something that practically everyone has experienced and known well." Yes, this is true in the sense in which you use the word, i.e. reproduction. There are also communes, religious communities, etc. And I don't believe that Marx considered the CMP (or any other mode of production) to be homogenous in terms of whether or not a surplus _was_extracted (or the form of surplus extraction).
IMO the point is that all other (still existing) modes have been subsumed by the global logic of capital. The family economy, in_ the_form_that_we know_it_ at least, is no longer essential to reproduction and is continually being whittled away (with the attendant antisocial externalties, if you'll excuse the expression) by the broader relations of production, a point made frequently by EP Thompson, Hobsbawm and others.
Perhaps at some time in the past, the "family economy" was the only kind of production. I'm not sure that can be said to have ever constituted a (dominant) mode_of_production (in the complete sense that Marx used the term), in itself. Or that we will ever know.
Regards,
Grant.