I don't have a direct answer to your post, but thought I'd chime in being a somewhat new traveling father. We have a 9 month old son who just recently took his 9th flight. We've flown with him on our lap every trip, but all domestic. I'm Gold, wife doesn't have status. We've been in F for almost all the flights, fortunately, since the extra room is nice when you're holding a baby for a couple hours. The 2 flights we had in Y was kind of a pain since it's so cramped.
I'm not sure if it's because he's flown so much, or we're just lucky, but he's never cried on the plane and barely makes a peep. On our last 2 flights, he was awake for all of about 30 minutes on each flight and slept the rest of the time.
Hope that information may be of use to you or someone else in the future.
BTW, loved that you signed the baby up for account the day she was born! My son doesn't have an account and I haven't bothered since we're going to lap as long as possible. Maybe I'll go ahead and sign him up if there are any new member sign-up bonuses.