Google Music All Access Family Plan for G-Suite / GMail Vanity Domains
I had wondered about this some weeks ago before finally trying it out today. I'm surprised nobody else had tried already. I was successful enough to be satisfied for my own uses. YMMV.
Result is I have a new Play Music account with Family Sharing which I can share with my G-Suite users, with all my playlists* moved over, and without anyone needing to maintain a separate email account.
This whole process took me about an hour, including moving across 15 playlists, but not including MX record propagation.