the solution to all this worry about missing middle names is to not call the airline and ask about adding your middle name. They’re always going to throw the book at you with a multi-hundred-dollar name change fee, because that’s the policy.
but the reality is that 99% of airline staff where it actually matters - at checkin and the gate - do not care in the slightest about your middle name. they care about reasonably quickly checking that you’re the same person as the document identifies and the same person that the ticket is booked for. throwing the book at you here makes their life harder for no reason. (Of course there’s the 1% that get a kick out of doing that...)
I variously leave off my middle name or include it, never had a problem either way. Once due to some Chinese airline’s terrible website I accidentally booked a ticket with my middle name as my last name and my last name missing. No problems that time either (but I’ll concede that I was very lucky with that one!)