Hi. I went through the ice mixed program, and did some of these same exercises. At the start, the hangs aggravated an old shoulder injury of mine (pain on the top of my shoulder). I backed off with the weight, and focused on hanging with my shoulder engaged, as suggested by Scott. After several weeks, combined with all the other training, not only was I able to hang pain free, but the pain from my old injury disappeared, and has not returned–I think the general and specific shoulder strength helped cure my old problem.
Couple of points:
First, if you are having pain, I would say, you have to back off, lower the number of sessions or the weight, or change something. This seems like an “of course” answer, but plenty of people might keep doing the same thing, push through the pain, and then get injured.
I second (and third, and fourth) the suggestion to “engage” your shoulder when doing hangs. How do you do this? I have found different means of explanation helpful:
1) Be aware of the space between the top of your shoulder and your ear–don’t let your shoulder rise and touch your ear. Keep your shoulder down, or keep space between your shoulder and ear.
2) Think about squeezing and egg or a tennis ball, under your armpit. This will help you keep your arm down. Come to think of it, you could even try to hold a tennis ball under your arm (trying to hold an egg might not be the best idea?)
3) Think about engaging your back muscles, squeezing your shoulder blades together.
4) Keep your elbow slightly bent.
In my experience, all of these things make the grip strength training harder. In some way, they transfer the hardest part of the exercise from the grip to other parts of the hand/arm/shoulder chain, which might not be ideal to maximally isolate grip strength, but in a functional sense, you are only as strong as the weakest link.
Hopefully some of these suggestions/visualizations/concepts will help you keep your shoulders engaged.
OK, good luck,