Good remix, not getting the dogfight feel though..
The original is too upbeat for that kind of thing. If you ask me, this sounds more appropriate for a Christmas-type song. Quite honestly, it sounds that way to me.
The brass and guitar are a bit too loud, and the drums aren't loud enough. I might suggest using a better rock-sounding kit. The rhythm sounds good, just not right on those drums.
If you want more of a flight/fight type thing, heavier drums, moar power guitar, more minor chords. This sounds good, but it doesn't sound the way you describe.