Here's my .02 for a trip...
I mapped out a loop on Caltopo that might meet the criteria you outlined. If you're not familiar with Caltopo, you can click on the "graph" icon next to each section listed on the left hand side and get a profile for that section (I'm on a PC...not sure how (or if) it works on a cell phone without using a web browser...). Keep in mind the distances calculated in Caltopo have not been very precise for me in the past. Anything under 5 miles I typically use a +/- of 0.5 miles and any lines over 10 miles I use a +/- of 1 mile.
Summary
Day 1: Elk Garden to Thomas Knob - 4 Miles
Day 2: Thomas Knob to Lewis Fork Wilderness - 4 Miles
Day 3: Lewis Fork to campsite subaruWx described - 3 Miles
Day 4: subaruWx to Elk Garden - 2 Miles
Caltopo Link
https://caltopo.com/m/RMFBC
Day 1: Elk Garden to Thomas Knob
Looks like 4 miles all uphill for about a 1250ft gain. Doesn't look like any slopes are super steep though. I've found decent hammock spots in the past on the wooded side of the trail between Thomas Knob and the Mt Rogers Split. Picnic table, bear box, and shelter (duh!) available.
Profile:
EG_Day01.pdf
Day 2: Thomas Knob to Lewis Fork
4 miles back downhill. Again nothing crazy. I recommend sticking to the Crest Trail over the Pine Mountain Trail. Last time I did it, the Pine Mountain Trail was not as well maintained and had more little rock scrambles and such. The Cliffside Trail to the Lewis Fork trail is well marked. The main campsite at Lewis Fork is right next to the creek. There's maybe three spots for hanging hammocks in the main campsite (maybe) but there are lots of trees around if you're willing to bushwhack it a little. I included a picture below of my setup from last September (that white rectangle in the middle is my tarp). No bear box, no picnic tables, no shelter. There were a couple of fire pits built last time I was there.
Profile:
EG_Day02.pdf
Day 3: Lewis Fork to subaruWx
3 miles uphill to where the hiking trail and horse trail meet up where subaruWx mentions a campsite and spring. The Lewis Fork Spur trail was well marked and cuts over to the Mt Rogers trail.
Profile:
EG_Day03.pdf
Lewis Fork Campsite
https://photos.app.goo.gl/ttjhjdP4LWgfis8XA
Day 04: It's jus t2 miles back to the car. How hard can it be?(.....duh duh duhhhh! <insert nefarious music here>)
I'm hoping to make it up there Friday (6/24) so be sure to post whatever route you guys might be taking. I'd love to come find you guys. One thing to be aware of for making plans at Grayson...every time I've ever included a horse trail in my route it has always ended up either being a giant rock garden, a mild river with the trail somewhere underneath the water, a giant mud puddle, or the combination of all three! I avoid them at all cost now if I can.
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