OK, after reading all this and adapting the info to my work processes, here's what I'd do. Remember, part of my process is I'm almost always working alone. So, I'd grab a 1x2, 3 or 4, just depends on what is handy. Use some good wood screws to attach it to the studs at the height of the boards bottom. Start in the center with one screw, lay a level on the top of the 1x and work your way to the ends, keeping it level with each screw.
Now that I have a solid support I'd put a couple of screws in my mouth, the drill/impact driver in my tool belt, pick up the chalk board and set it on that support. Grab the impact driver from the belt while holding he board on the support with my shoulder and shoot the center screw in the top. Finish with the two end screws.
Grab a cool one to celebrate.
It's not always about the finished result, it's how you get there!