You'll only need a JAA ATPL if you want to fly for a European airline, other wise your FAA licence will be fine. It's acceptable at Cathay, SIngapore and Emirates as well. The FAA ATPL is much much cheaper. However, for an American major you'll probably need a degree. You won't need a degree for Cathay but you'll need a fair few hours, ideally in turbines.
Which degree? Not knowing the US scene too well, I would probably look at a science or economics based one versus humanities. So pick a topic you enjoy and study that. You may want to ask those US airlines what they prefer to assist you there.
Every one's situation is different. One idea would be to do the degree full time and get your PPL in the holidays. Then go for it full time when the degree is done.
There's many ways of achieving the licence and your degree.