So you set the sensitivity to the maximum value but the bars still wouldn't move very far?
Yes.
Did you try turning the plane by rolling to the side and pitching up, or were you relying on the yaw exclusively?
Mostly with the latter. I tried briefly to do the former and then I gave up. Now that you mention this I started the game again and tried more seriously. I realize what went wrong. I wasn't doing a perfectly straight vertical movement with the mouse, so it made the plane move in a very wobbly motion which is impractical for turning. With a little bit of practice I could get used to it though.
Maybe you could try emulating a virtual joystick that you have to move by holding down a mouse button (like how you control the tank turret in "Gunner, HEAT PC" if you played that game). It would make some maneuvers easier than by dragging the mouse in a perfectly robotic manner.