While I aesthetically like that version, it has been pointed out elsewhere that when a flag is displayed on a travelling object (e.g. an airplane) the blue field is to be toward the front of that object. Unless eagles fly opposite the direction their beak points, it would seem that the flag in both pictures is 'wrong' (though aesthetically I'd say it's right on the right-facing eagle).
Actually, I think it might be even better to do as you say. Leave the flag as it is, point the eagle to the left. That way, the flag will have the impression of flying, which is probably the point of your flag etiquette point. And, also, we could simply say that the eagle is COMING from the right direction!