Oh, I found some stuff that might be useful:
forums.catholic-questions.org/showthread.php?t=52772- this is an “ask an apologist” answer from this very site, which basically says husbands and wives should discuss things and go with whatever seems to be the best option. It also says that the roles of husband and wife are not absolutely defined in the Catechism because for the most part, they just aren’t absolute; the spouses should divide responsibilities according to who is most suited for the task. It also says that wives are not subordinate to their husbands.
jimmyakin.org/2004/04/spiritual_heads.html- This is an answer from Jimmy Akin that says basically the same thing, but with more elaboration and bullet points. Unfortunately, it affirms that men should be the “spiritual leaders” in their families, without really saying what that means.
So while I’ve ruled out several things that “spiritual headship”
isn’t, I still have very little idea what it is. :ehh: