I hate to self-reply, but I thought about this while I was in the bathroom. That's where we get our best thinking done.
If you want to see how Captain America should be handled in a movie, go check out Eric Trautmann's The Shield from DC, which recently ended publication at #10. For some background, this Shield is an update on the original Golden Age character, who predates Captain America by a few months and is the first "flag" style hero in American comics. Anyway, this version of the Shield is Lt. Joe Higgins, United States Army, who is badly wounded and near death after an RPG ambush in Afhganistan. He is given a nanotech warsuit which bonds to his skin and makes him essentially a living combat computer. Lt. Higgins is a supersoldier in the employ of the US Army. He has no secret identity (the leader of his project, General Latham, says "The mask is for protection only. We do not hide the face of American soldiers), and answers to the Chain Of Command.
Higgins is deeply patriotic and proud of America. He gladly serves his country. There is some political machinations going on around him, which Latham typically handles (there's a great bit where Latham is sending a comminique regarding General Sam Lane, saying that there is no way in Hell is going to use the Shield for his insane agenda.) At the end of the day, though, its the Mission which is what is important. Really reminds me of the old saying that "A soldier has the benefit of looking his enemy in the eye." Defending America, her people, her interests, and those who need defending. He's brave, intelligent, cool under fire, a good commander and tactician, and supremely confident in himself and his team.
That's Captain America.