Well, I'm going to answer my own question because I'd like to see one here...
Kudos to JB Nizet to solving this for me/pointing me to the right post, here: Understanding annotations and JPA(hibernate)
The key is that the inverse relationship must be set. In the example above, to fix it:
player.setTeam(team);
playerb.setTeam(team);
Once both sides of the relationship are set, then it's persisted to the database.