Your idea is exactly what I would do and I have mounted hundreds of TVs. I have mounted lots of larger / heavier TVs on drywall only with high quality anchors. Hit that one stud and it will carry the lion's share of the weight, the anchors will just keep it nice and flat. Just make sure you really hit the stud!
Don't just trust a stud finder. Drill a series of tiny holes horizontally so you know right where the center of the stud is. You can also just poke a finishing nail or etc through the drywall. These holes will be behind the mount so they won't be visible. (If you ever remove the mount you'll have to paint anyway.)
Use 1/4" lag screws and washers, washers are important. Drill a 3/16" pilot hole for the lag screws. Get it tight but not so tight it deforms the sheet metal. This only takes a few minutes and will make it as strong as possible. These two lags could carry way more than the weight of the TV.
Now in the corners, I have a specific product suggestion:
I'd use the Snaptoggle BB, the 1/4" size. You could probably hold the mount and TV with just these without hitting the stud, but it's safer to hit the stud.