Have you tried using the Thrustmaster 1 setup? That has everything you need mapped.. and since you have the T.Flight Hotas X, you can manually switch buttons using the joytsick if you feel the need.
Aye, deadzone is one of the annoyances I have found, it can be quite fiddly to make small adjustement.. I actually found the normal controller was better for this particular thing, even in realistic or sim mode. Yeh, the rudder is quite sensitive too, and if you press it too much it springs back making you spray your bullets all over the place anyways
I made a post
here about my thoughts on using the T.Flight Hotas X with BoP.