I believe video over UTP baluns should be pretty easy to find; but I don't know how they'd work with CATV - they are usually meant for CCTV applications.
Would not work. Too much loss over the twisted pair at the higher frequencies used by CATV providers, which can go up to 1GHz.
CCTV composite video has bandwidth less than 5MHz which is why such baluns work since loss at 5MHz is relatively low on the twisted pair cable.