There are options here; you could avoid opening the wall if you don't mind looking at some supporting structure on the exposed wall behind the TV. I am assuming you want to avoid that for the sake of the finished appearance. It very well may look nicer that way.
But if you want to use a single-stud style mount, that is going to mean opening up the wall. Note that with a single stud mount, you need to have attachment points that are spaced along a vertical line. A horizontal 2x4 block is not going to work.
For these reasons I would say adding a full height stud (vertical) is really your best bet. The mounts that attach to a single stud usually have three bolts and must attach very securely. If it's an articulating mount, the cantilever when the TV away from the wall puts a lot of pullout stress on the fasteners, especially the top one.
All you will have to do is toe-nail the stud into the top and bottom plates where you want it. It will be cheap (maybe $5?) easy, and secure. You'll want four 8d common nails, two on each side.
Toe nailing can be a little frustrating until you get the hang of it, and it can be very difficult if there's limited space. You could use screws instead of nails, but should at least use special "structural screws" or "construction screws" - not ordinary deck screws, and definitely not drywall screws. Since this isn't holding up your house, just your TV, you have some latitude. With screws, you can probably toenail the bottom in place without removing your cove molding.
Re-reading the question - it looks like you want to install a horizontal block or blocks. That works if you install two horizontal blocks with a vertical block between them. This can be done with a smaller hole in the drywall.
I really don't think there's much difference in the work involved in a big 16" x 8' drywall patch versus a small 16" x 2' drywall patch. However in this case, the small drywall patch may be less noticeable behind the TV, if the patching is less than perfect and visible.