A few things that should help make your job easier.
Extra long drill bits - They make them in various sizes both in hole size and length. I like the 72" long versions since that will go from the hole in the wall through the top rail board for that wall. Often these long ones are designed to bend easily (but may require a holder so you don't burn your hand from the friction) so you can stick it in the hole and bend it 90 degrees so you won't be on the floor trying to force the bit. Often they also have a hole in the bit for attaching the wire to help pull it into position.
BES 1/2" x 72" High Speed Steel Flex Bit (altex.com)
Fish rods - they are designed to pull the wire where you can't easily go. They have many different types but generally they're the same basic design with the difference is the length. Often they're six feet long and screw together to make it go the length you need. It's best to get a kit that will do the job but when you do buy one that has matching individual or pairs so you can later extend it further if needed. They also have different ends to attach the wire since one type may not work for your situation while another will be perfect.
BES 6' Replacement FiberFish Rod (altex.com)
Low voltage mounting plates - Instead of using electrical wall boxes you might have better luck with the special low voltage versions that simply line the hole in the wall. This will allow you to route your cable(s) more easily than forcing them through the holes designed for electrical wires. They make both single and double sized versions but the single should handle most of what you need unless you have loads of wires.
Plastic Single Gang Mounting Plate (altex.com)
Wall plates - There are many options here, some are ready to use and others require you to customize them to your specific needs. You can get a standard blank wall plate and drill the hole to fit your coax or feed-through connector. This is the most complex way to do the job but if you're careful can be the best looking option. They make wall plates for network/CATV/AV use and depending on your needs may work well. They make plugs for standard "F" connectors used for cable TV use and standard BNC for AV use (often these are 75 ohm though!). You could even just push your cable through the hole and be done with it. What I like are the "bulk cable" versions. It allows several cables both large or small to fit through the hole and angle it down towards the floor to make routing easier.
Vanco Bulk Cable Wall Plate (Single Gang) - White (altex.com)
