Putting TV cables inside a plasterboard wall cavity - Is my plan reasonable?
I see no real reason to add in the new stud box to allow for the TV signal cables to have their own cavity. You should be able to simply mount the flange on oneside of the backbox to the stud and use some type of toggle anchor to simply attach the other flange of the box to the drywall. Using this technique you should be able to simply cut two holes in the existing plaster board without having to remove and replace a large amount of material.

I do see two concerns though:


It is not up to standard electrical codes to string TV power cords or extension cords up through a wall cavity like you can do with low voltage signal cables. You really should plan to install separate permanent in-wall mains wiring from the existing power outlet up to a new electrical box and outlet that you locate behind the TV.
From your pictures it looks like the TV mount that you are planning to use is one that mounts to only one stud. If that mount is an articulated arm type designed to allow the TV to fold out from the wall then I would strongly suggest that you look for another type of mount that installs across multiple studs. If the stud locations are not in a good location then face that wall section with 3/4 inch thick plywood that does span two to three studs and mount the bracket to that plywood.