I don't know where you're getting this "limited supply of buttons" business from honestly. Which CH stick do you have?
There is no need to combine devices for Aces High (you usually do that for games that don't support more than one controller, Aces High does), and there's really no need for different modes either. Fighters and bombers have the same controls, and vehicles are driven with the keyboard and mouse these days. Besides, you make things harder for yourself trying to keep track of what button does what on which mode.
In fact, there's no need to use the CH Control Manager at all for Aces High unless you really want those "complex functions."
Honestly the best way to do it is leave CH Control Manager in "Direct" mode instead of "Mapped" mode and map the controls inside of Aces High. That's the way I did it in AH with the full CH setup (Fighterstick, Pro Throttle, Pro Pedals). Even with the CH Combatstick (which has one button in place of a couple of the 4-way switches that the Fighterstick has) has plenty of buttons for your immediate flight needs.
As far as what control should go on what button, of course that is personal preference besides the obvious primary fire/all fire on the trigger. I might also recommend flaps up and down on the top and bottom of the lower 4-way switch on the Pro Throttle, but even there I personally decided to put flaps up on the TMS (target management switch, the left hat on the top of the stick) simply because I could push that faster than I could push up on that hat on the throttle, so it's all up to you.
The best place to start is, if you haven't already, go to Map Controls inside Aces High and read what EVERY control does. All of them. The better you understand the controls the better off you'll be, period. There are a few controls that might confuse you such as CM Eye, you won't have to worry about them. But if you ever want or need to know what something does, DO NOT hesitate to ask.
Once you've got an understanding, you can decide what you want on what button.
If you really do want or need those "complex functions" though, let me know and I can help you with that. To use them, you'll have to switch CH Control Manager to "Mapped" mode, which assigns custom names to the controllers as the game sees them. So if you start mapping controls in AH while in Direct mode and then switch to Mapped mode, the game will see them as different controllers and you'll have to start over assigning controls to these "new" controllers.