Without seeing your dough recipe, it is hard to say exactly what is happening to your dough. It could be that you have been underhydrating it and that has led to a stiff dough that is hard to manage. Remember that a high-gluten flour can tolerate a higher hydration (more water) than bread flour, so if you didn't adjust the water upwardly when you switched to the high-gluten flour, it is possible that that was the source of your problem. If you didn't coat the dough ball with a bit of oil while it was in the refrigerator, it is also possible that the surface of the dough dried out and made it difficult to reshape. I normally don't reshape the dough after it goes into the refrigerator, but were I to do so I would simply press the dough to allow the gasses to escape and gently reshape. Again, this can depend on the recipe and how and when the dough is to be used. Some doughs can handle more than one punchdown better than others.
As far as knead time is concerned, that depends on the dough formulation, mixer speeds, and the quantity of dough to be kneaded, among other factors. So it is hard to specify a specific knead time. Seeing your dough recipe might provide some clues as to whether you are trying to knead too much dough or if you are overkneading the dough. It is possible with a mixer, even a KichenAid mixer, to overknead a dough, but it would take a lot to do that.
If you can post your specific dough recipe and how you practice it, in detail, maybe we can find the source of your problem.