Your plan should work just fine. I did this during the last week of July after a good snow year and had no difficulty.
The only thing I'd suggest is to go beyond Mistymoon for your first night. If you can do another 2-2.5 miles you'll be better off. Head towards Lake Solitude. When you're above the big wet meadow (you'll know it when you see it) head toward the falls. You'll find the climbers trail at the top of the falls. I have no idea if this trail is easily followed or not because we went at Cloud Peak from the opposite direction. BTW, there's a good spot to camp about a half mile above the falls in a small meadow. This is where we first found the climbers trail if memory serves. Anyway, If you lose the trail don't worry---just keep following Paint Rock Creek upstream until you get to the first stream coming down from your left. Follow that stream up a very flat but wet bench. You could also camp up on the bench.
From this point it's basically a walk up to the summit. We did it in about 3.5 hours but with a lot of pecking off along the way, made it back down in less than an hour. From the flat but wet bench you've got about 4-4.5 hours back to the trailhead.
I"m not sure if you'll have the time to see much else while you're there but if you get the chance stop at Pistol Pete's in Buffalo for their breakfast burrito smothered in green chili. I'm not sure where you're coming from but if you've got the time you can't go wrong driving through Shell Canyon, Tensleep Canyon or stopping at the Medicine Wheel.
FWIW, I've never hung my food in that area of the CPW
photos:
http://www.dorfworld.net/backcountry/ba ... hotos.html
So many mountains, so little time.