Another update. I am very happy with the Dish Hopper bluetooth feature now. I can turn it on and off whenever I want and the signal is very strong. I measured out 41 feet, the longest distance I can get from my TV and still be relatively line of sight, and it still had a strong signal with no static or interference.
I did get the new Slingbox and connected it to my Hopper and it works great, and the bluetooth feature still works, so it must have just been the bad Slingbox causing the previous problems.