Another technique.......
All of the above is true, but there is always more than one way to 'skin a cat'.
I had exactly the same problem and my instructor, having failed to fix my control reversals, was on the verge of chopping me when he flipped his strategy.
He took me to the hover squares and told me to 'stir' the cyclic in a pretty rapid and constant circular motion whilst he did pedals/collective, the point being to adjust the centre of the cyclic circle to prevent drift and remain inside the square.
What ensued was initially both ugly and uncomfortable, but instantaneously effective. Because I was stirring I was avoiding the reversals and, due to the speed of the stirring, no single cyclic displacement had any positional effect (other than to make us nod in unison). All I had to do was incrementally (and subconsciously) move the centre of the circle to maintain the desired hover position.
All that remained to do was to reduce the diameter of the circle until my subconscious brain got the hang of doing it the proper way, then add the pedals/collective back in.
Probably not a recommended technique, but talk it through with your instructor. It may help.
Thanks for bringing back that memory, seems like a loooong time ago!