I really like the comments that Louis, Bob, and Fumin have made. Having had the benefit of their comments, I would like to return to a portion of your original post:
"As one of my warmup exercises I rotate my neck. I try to be mindful of Taijiquan principles: to let yi guide my rotation...."
For me, this is a critical point. I am not sure what you mean, but I do not think of Yi has something that is added to motion, but rather something that defines motion. For me, Yi ("intent") should have something of Yi ("meaning") in it. When you paint or do calligraphy, you do not think of adding Yi to your movements, instead Yi defines, shapes, and motivates the movements.
If you do neck rotations and subconsciously imitate some motion someone has shown you or even an ideal motion in your mind, I would question whether your Yi is really correct for the purpose you describe. If on the other hand, your intent is to circle and loosen up the muscles with each micro-movement, you will move slightly differently. Then I would say that you are really using Yi.
In any case, I have read admonitions against full neck rotations similar to what Louis describes and no longer do them.
I can also add that in Association seminars, we also sometimes do brief simple warm-ups, stretches, or limb shaking, expecially after a sitting break. These motions are not in any Tai Chi form I have seen and yet seem acceptable and useful.
Welcome to the Board,