Hello, not sure what causes the problem with logitech controllers. May I suggest you to set up the keyboard for the moment? Also, can you try to make a shortcut with the /OLDPAUSE command and see if your controller works in special stages with it?
Right click the game and create a shortcut.
Right click the shortcut and select properties.
In the properties window into the destination tab after the quotes add /OLDPAUSE.
Hit OK and play the game through that link.
Warning: in OLDPAUSE mode you get out of pause by pressing ENTER on your keyboard, no matter what your controller configuration is.