One of the best ways to address the full spectrum of function in string playing is to work on audiation skills, or developing the aural imagination. I find that physical tension is often related to an lack of internal clarity with pitch and rhythm and even more abstract concepts of dynamics, phrasing, and articulation.
Feldenkrais said, “If you know what you are doing, you can do what you want.” I would say for musicians that if you can imagine the way you intend for something to sound, you are a big step closer to doing what you want.
So, get your vocal cords warmed up, because there is no better way to work on audiation than through singing! This TT is full of brain-teaser style exercises for combining singing and playing. I use Lightly Row in D Major as a model, but these exercises can be applied to scales and/or samples from any level of repertoire to develop you internal aural world.