You'll have to look at how Amex points convert in the US to see if that helps you with you BA/AA/US travel situation.

As for travelling with an infant, it depends. We've been through four of then and the worst age to take them flying is between 12 months and 2.5 years, as they are too big to just lie there and sleep, but too small to be allowed to walk by themselves. At 15 months you may find yourself chasing an eager walker up and down the aisle on an overnight flight. Stops being cute fast!

I think a front bulkhead seat is the way to go. You probably won't be relaxed enough to enjoy the business cabin.

Welcome to FT!