I get the desire to be put in the action, but you still need to give the player a way to exit your game. It can be diegetic (like quitting the game is literally an exit in the game), but it still needs to be there. Asking the player to Alt-F4 to quit the game is a bit much. If you want to make sure the player isn't getting an advantage while paused, you can keep the game running in the background while they're on the menu. If you keep the game running while in menus, make it obvious to the player.
As for the controls, I'm not quite sure. I think if you put the fire onto the trigger, it'll be more inline with twin stick shooters. That would certainly open up the thumb to focus on the camera. Another option would be to put pan left/pan right on the shoulder buttons. That's more in line with old 3D games. I'd play around with the controls and find that sweet spot where you're not overloading one thumb.