With recalibrate I mean the "move stick to center, now move in a circle, now back to center....etc"-process and I think I tried it with and without Saitek drivers, didn't seem to make a difference.

I personally think the idea of two joysticks sounds a bit weird, heard it before though, but if the throttle can go four ways...
The dedicated solutions are also full of additional buttons and sliders which may be useful, but like I sadi, currently I'm concentrating on other games anyway.