I'm ecstatic to report that our flight was a dozen times better than I ever expected it would be! My little monkey slept the whole flight!
Some friends suggested I take the carseat on the chance that there was an empty seat and they'd let me use it. I hoped and prayed and lo and behold, Eli got his own comfy window seat! He was wide-eyed during take-off, looked out the window for a couple minutes, and then quietly nodded off. He slept until just before we landed. The flight attendants were amazingly helpful and even brought Eli his pair of wings!
Now on to hoping and praying the flight home is as easy as the first was.