Reddit mentions of Linville Gorge, Mount Mitchell [Pisgah National Forest] (National Geographic Trails Illustrated Map (779))

There's no trail shelter at Deep Gap. There used to be one but it was removed decades ago- so you may be using an old map or basing your itinerary off outdated information. Alternatively, you may be confusing Deep Gap in the Black Mountains with a Deep Gap on the AT, which does currently have a shelter. Assuming that you haven't already done so- my first recommendation is that you invest in a new map ASAP. The National Geographic Trails Illustrated Map that covers both Linville Gorge and the Black Mountains (including Mt. Mitchell) is a good one.

There is room for tenting in the Deep Gap on the Black Mountain Crest Trail; it's been a few years since I was there but I recall there being a decent tenting area. There is a seasonal spring located maybe 100-200 feet down the Colbert Ridge Trail, but I don't know how reliable this is year-round- I probably would not expect to rely on it outside of Spring.

You mention starting at Shuford Creek- I haven't hiked north of Deep Gap but I've heard stories/read trip reports that indicate that the trails to the north are pretty overgrown and poorly maintained. For what it's worth, I found the Colbert Ridge trail to be well maintained and easy to follow when I hiked it in 2014, so you might consider starting at the Carolina Hemlocks campground instead.

Another advantage to starting at Carolina Hemlocks is that you can make a loop out of it. Climb to Deep Gap for night #1, continue south over Mt. Mitchell and camp at the Commissarry Ridge backcountry tenting area on night #2. On day #3, take the Buncombe Horse Trail back to the trailhead near Carolina Hemlocks. Alternatively, if you make good time on day #2 and want to continue further before camping, there is a nice (but exposed) campsite on Maple Camp Bald, and another campsite located further down on Maple Camp Ridge (although this second site may be hard to find in the dark if you don't get there until late). If you make really good time, there is a nice campsite where the Buncombe Horse Trail crosses Middle Creek, located a 100 feet or so upstream of the crossing (this site has the advantage of having the creek immediately adjacent as a water source). The Buncombe Horse Trail did get a bit brushy between Maple Camp Ridge and Middle Creek in 2014 when I hiked it, but I did not find it to be a significant navigational challenge. There is 1 or 2 unmarked junctions to be aware of where the old logging road that the trail follows splits without signage indicating the correct path. I just picked what appeared to be the most well-traveled path at each junction and had no issues with losing the trail.

Overall, the climb up to the ridge via any trail is long and sustained but if you're in decent shape and have backpacking experience it's not a major challenge- just budget the time for it and keep up a slow but steady pace. Once you hit the ridge it turns into a fairly pleasant walk. There's some moderate ups and downs as you pass from peak to peak, but in comparison to the long climb from the base of the range these feel hardly perceptible.

Another thing I will add is that if you plan to camp at elevation, be prepared for cold nighttime temperatures.

I hope this is helpful. Good luck, and have fun! :-)