score:2
I think I know the answer now. I wanted to complete all the applications before paying, so I filled them all in. I noticed that the payment information for my children said $0, whereas for myself and my wife it said $25 (application fee). I gather it gives the cost based on age not on whether you are linked to someone else's application.
I hit Submit Application here and it tells me the application is in progress, same as it did for my wife and me, but without requiring CC information first.
So it appears now I'll pay the $82.75 each for my wife and me, and $14.50 each for the two of us plus my two eldest children as they're over 14. Way better than $122.25 each for 6 of us.