Ideally your hand should be leading the racquet when you hit a bh volley or a bh slice, so it's not really necessary for you to stabilize the frame with your thumb running up the grip. Imagine pulling the racquet down and forward through the ball - you're better off with your thumb wrapped around the grip to help maintain a firm hold of it.
To help find your power source for that volley, try having someone send you some easy feeds while you hold the racquet up on the throat just above the grip with that same (hopefully continental) position. Placing your hand farther up the racquet like that will make is harder to be wristy with your volley. Keep your arm rather quiet with only a mild forward move through the ball as you make contact.
Look to power the racquet through the ball mostly by pushing off your back foot and moving forward onto your front foot. If you're turned sideways for that backhand volley, this move is sort of a deliberate side-step toward the net. Instead of swinging the racquet with your arm as you would with a ground stroke, your legs create the motion to drive the racquet through the ball for a sharp volley.