Thanks for all the replies! I didn't realize I could get on a Singapore flight TATL. How do I build that in an itinerary? I didn't see it as an option when I was booking on lufthansa.com and I can't select the US as a destination from EU on singaporeair.com, either.
I hadn't considered the number of options over here. My choices seem rather limited with SkyTeam to Alitalia (no way), Air France, and Delta. I'd love to fly Swiss or Singapore if I can figure that one out.
I'm flying back to the US in about a week on Air France. All this promotion of Lufthansa over AF has made me look at switching. As luck would have it, I can cancel/refund my AF flights and get on Lufthansa for net $5 difference.