If you get to the point where you are experience actual pain -- headaches, muscle cramps -- or have abnormal heart rate or breathing, then stop. Stop if your extremities become numb or difficult to move. Otherwise, if it is just uncomfortable, unpleasant and your heart rate is within the range of strenuous exercise, that's normal. I think that most of the benefit comes after the first 3 minutes so I try to aim for at least 5, ideally going to 7 minutes. I also keep rotating to expose all my most sensitive parts, which in my case include my neck, shoulders, hands, the top of my head, and my chest.
I think your idea of exaggerating the shiver is an excellent idea. That should help the thermogenesis as well as making the cold more tolerable. Most likely, you'll find the need to do that will diminish with time and experience. Another approach I use, especially at the beginning, is to grit my teeth and stiffen myself to the cold. I also find that laughing or singing helps. I think these are all forms of "compensating" that are quite helpful.