I experience the constant feeling too, and as if it spreads out a bit. I feel my hand perhaps made stiffer than it is in a normal relaxed state. I don't know exactly what we can learn, but it's one way to understand how the contraction/relaxation dynamic works. As for speech, I practice reading out loud focusing not on anticipation, but in relaxing my neck, i.e. alleviating any arising tension that is created by words I already read out and utterances already made. The more I am regular with my practice, the more I can do the same in interactions with others. It's an effective way to shut down anticipation. It comes out a bit weird as I explain it though. I don't know if it reads as intuitive to you.