Wow, that's a lot for 2 weeks. As others have said, United is best. You can avoid the high fuel surcharges associated with BA Avios if you can find availability on Air Berlin (searchable on aa.com but you'll have to call BA to book). The downside is they only fly to select U.S. cities (LAX,JFK,ORD,MIA,RSW), and from there to Germany (mostly DUS and TXL). So you'd have to fly from DFW to one of those cities, then to Germany, then from Germany to your European destination. So that's two connections, minimum. So United is the best option.

Also, as you saw, flying back from London will always have a moderate surcharge (~$150-$200). For that reason, I would recommend flying to London first, working your way south, then flying back from Rome.