RG6 to RCA & balanced audio to RCA

I was talked into running an RG6 and a balanced audio cable (2 conductor with a ground) to a location for an undercabinet TV. The LCD TV only has RCA connectors on its inputs.

First I need to find a mocular (snap in) connector that takes RG6 on the back and an RCA plug on the front. I have found a non-modular one in the Leviton catalogue in it's own full size faceplate but cannot find a snap in equivalent. So if anyonje has a source fot snap in types, I'm all ears.

Second, is there any way to attach the balanced audio cable to 2 seperate RCA jacks without having to solder on extra ground wire to the jacks. (there is only 1 braided ground in the cable.

Third, what is a better method of cabeling for composite video and L/R audio in the future?
Couldn't you just use a F to RCA adapter on the TV end and run a coax with F connectors on both sides for the TV? Then you just need the standard F female-female snap in.
Thanks for your suggestion, but this TV is an undercabinet mount that folds up and swivels. In the past, the stiffness of RG6 causied bunching in the cable routing and possibly getting caught in the mount when it folds.

I would like to use a 3-wire WHITE/RED/YELLOW premade RCA cable to feed the TV because of its flexibility.

Any tips on splitting tha audio cable between 2 jacks?