Yes, in-flight background music takes away the seriousness in a combat flight based game. It makes the game aracade-y. Same goes for racing sims. Even 'lite' sims A-10 Tank Killer and F-29 Retaliator don't have in-flight music.
I'm a flight junkie myself, have a collection of flight sims.
I'm surprised you didn't mention Falcon 3.0 (Or maybe i missed reading it?) The manual is like the telephone directory of yesteryears.
Others of interest were TFX, EF2000, SU-27 Flanker.
I also used to play F-117A Nighthawk and Gunship 2000 a lot those days.
EDIT : The best part of these games is the landing! The excitement and tension is even more than the encounters themselves!
And the most unforgiving and brutal landings I could ever think of is in F-29 Retaliator. Crazy!