This is not a problem of a twisty stick by default, it's more the way that Logitech decided to do the stick forces. Simply put, Logitech twistys need very little force to "engage" the twist, so little in fact, that, as you said, apply rudder basically whenever you move the stick.
Now with Saitek twistys, it's a completely different story. They need a lot more force to engage the twist, so there is no accidental applying of rudder at all - as it should be.
I'd give the Saitek Cyborg X a try. A very good Joystick for it's price range, and beats evertythig Logitech offers in that range hands down, in many ways.
the cyborg x is not a bad stick at all.
i'm sure you can get your logitech working fine though with the right settings. this is how i setup mine.
i use pedals so i dont know if this will translate well to a twisty since a twisty has less range of motion.
the x and y axis are identical
setting the scale flat across the board at 40% allows for
steady fine tuning control when you're doing normal combat manuvering. with this setting you STILL get full range of controls at full stick deflection though there is a jump at 90%. not noticeable when you're jamming the stick in that manner anyway.
my rudder is at a lower scale because i want even more control at the lower end. the deadband and dampening is turned up a little because the center is stiff... this might help with your twisty axis though i would really prefer my rudder to not stick in the center so i could leave deadband and dampening off.
this is a mix between default scaling and scaling off, and i really believe this is the best of both worlds. giving good low end control and smooth flat line scaling.
oh, and the one thing i hated about the saitek stick was the physical dead zone that made the stick feel loose in the center. my quick fix was to super glue the twisty axis and that put and end to that crap!