I agree that if the way you grip is making a difference, it is more an effect of how relaxed or tense your grip may be at putting pressure (without the player obviously aware) on the embouchure.
As an example: I use to find that after reading posts by Kingtrumpet, I was putting a choke hold on my trumpet. At that point in time, my sound would become puny; but then when I visualized KT turning blue than passing out, I would relax the grip, and play with such open, light hearted lines. It was almost euphoric. This has taught me to work past my anger, lesson my grip. So thanks KT, for providing the insight that has made me a more relaxed player, now that I have worked through my anger.