You've made an excellent and very full trip plan. I tent camp about 30 nights a year in the region off of motorcycles, and take groups into the region's attractions regularly. You will encounter no problems at the National Radio Astronomy Observatory carrying a weapon. The ONLY hassle I've ever had in WV has been from deputy sheriff's, three occasions, twice at gas stations, once at a diner. The Fed lands all follow state criteria, state parks are OK, regarding carrying.
On federal forest land, [and most other federal property, unless posted to the contrary] you can engage in "dispersed camping"; off of forest service roads, pick a spot and camp. Down side with a group is no facilities at all, potable water, etc. I have found the most accommodating and least expensive camping to be at Seneca Rocks, and it is a good staging area to hit all your plans from. At Seneca Rocks, along with the rocks, you'll find The Discovery Center, a Forest Service operated information center. At the heart is Yokum's Vacationland and Harper's Store. Yochum's offers two camp sites; Princess Snowbird across from the General Store. It gets inhabited by the climbers, gypsies, carnies, and other riff raff. Up the road a half mile to the north west is Yochum's Stable, Motel and Restaurant. They also have a camp ground along the river. Kind of a "best kept secret" of the area. $6.50 a head to camp, pick your spot. Their grandson comes through with a pickup loaded with firewood. Ten bucks will get you all the dry split wood you'll need for a couple of nights. Shelter house if things turn ugly, showers, and your stuff is safe if you stage out of there. The river is too low now for tubing, rafting or swimming. Yochum's has an indoor pool. Above Harper's Store is an eat joint with fantastic sandwich menu and pizza. Yochum's still have rooms available, from 45 bucks for the basics to 70 bucks for room with kitchenette. You are 25 minutes from Spruce Knob, 38 miles +- from Cass / Green Bank.
A unique evening experience might be 30 mile trip north to Thomas, and the Purple Fiddle. Good food, coffee, music and if the weather goes south on ya, twenty bucks a head puts you in a bed under a roof.
You have a pretty full schedule. Marlinton, Cass RR, Green Bank Observatory and a trip through Snowshoe will wear out an Olympic athlete. You didn't mention the crown jewel's of the Monongahela....Smoke Hole or Dolly Sods.