It's hard to find a nice round trip schedule in one airline that fits your needs. With that many miles I would book United one way, AA the other way. I just did that for my december, 2 week trip to Argentina (im from there) and it was impossible to find roundtrip that fit my needs (2 weeks or less). I ended up booking economy there (the dates worked better) and business/first class back with LAN. Flying out of EWR, into JFK.

Also, milevalue explained that sometimes you can trick United website to show you business/first class availability by first looking up a low season date and then click the calendar to move forward till you have seen the entire 11 months forward. United is more likely to show you availability this way.