The fox at towing speeds inverted will start to stall and carry on if you push the stick too far forward as you have worked out.
So when you are rolling the nose drops and then once you are inverted you have to push a lot to stay behind the tug, which in turn is causing all of the wing drops.
If you pull the nose up before rolling, and then also add some top rudder when the wings are going through 90 degrees to hold the nose up, you will require less forward stick to stay in position behind the tug. It is then a little easier to control. Here is my example: https://youtu.be/bBWm2SLlpbY
Hope it helps?