I have the same stick Puller,
I noticed that if I didn't have the logitech software installed, I too experienced poor/erratic feedback. Since I installed the software, I only have to re-calibrate upon starting the game for my own feel-good-ness.
I know that I also have to un-plug the joystick when playing certain other games (Xcom) because there is a conflict occurring with USB mouse and USB joystick inputs. May i suggest verifying that your joystick behaves properly outside of the game? As in, do you see the same type of "hang" in axis movement when outside of the game?