Hello Leigh,
I think you've sketched out a perfectly delightful drive and one which can be done at a very relaxed pace. I have not driven VA 42 from Buffalo Gap to VA 39, so I am envious of your plan to take that drive through the Alleghanies.
I believe the Warm Springs Inn is housed in a converted gristmill and has a small restaurant/cafe'/bar attached. Warm Springs is a very small village, but Hot Springs, with the Omni Homestead Resort, is just 5 miles south down US 220.
I LIKE the idea of driving down VA 600 to Lake Moomaw. That's another piece of the Alleghanies I have not seen. If I'm not mistaken, it's a gravel road, or at least the far end of it is. But no worries, graded gravel roads are traversed by standard automobiles all the time. And you should have no difficulty in reaching Harrisonburg along I-81 towards the end of that day, though you'll probably want to plan on a somewhat early start from Warm Springs, where I'd guess the Lake Moomaw out-and-back would run at least 2 hours, perhaps a little more.
The only other thing I'd suggest is to allow for some DC area traffic congestion on your final leg from Harrisonburg to Dulles. That can be challenging even in the middle of the day.
Best regards,
Foy