So, do you have any best practices to share for dealing with this sort of situation? Let's assume that for whatever reason, you can't avoid the issue entirely by praying before or after the flight, as some suggested in the comments on the news story. How do you put on talit and tefilin in public (especially in confined travel situations) and minimize the potential for freakouts by the people around you?
Don't pray audibly. Do as Chana did: Lips moving, no one hearing.
Alert an authority: "Hi, flight attendant. I'm Jewish. Our men (and perhaps some of our women?) pray with little black boxes on our heads, straps on our arms, and a big striped shawl. I'm going to pray now. We try our best not to interrupt our prayers for talking or anything in the middle. I know it might look a little crazy, and just wanted to let you know."
My father always says -- don't go there. If the only time for praying is on the plane, do that without talit and tefilin (I don't think anyone will really mind if you're whispering out of a book), then put on talit/tefilin at home/synagogue/hotel room later on (assuming you'll have time for that).