Thanks for all of the great suggestions and things to think about Devin!
The land is 7.5 acres, about 350 running E/W and 950 or so running N/S. It is completed wooded save for the tiny spot the dome sits on and the very small clearing at the front of the property. I am opening up the clearing a bit more, mostly small trees that have grown up over the past 10-15 years since the previous owner stopped really visiting. We will do some selective removal around the dome for safety issues but won't be opening it up too much. Plan is to build 1-2 more tiny cabins on the property. I doubt I'd ever need to cut trees for firewood, there's enough fallen/dead stand to fuel a tiny wood stove for years to come!
I'll be having a forester come out this summer to survey the land and get more information about the trees, tree age, etc and to submit my timber designation to reduce my property taxes. My stepdad walked the property with me and has been there a few times prior over the years and knew some of the history with tree age, remnants of a fire from the 20's, etc. It's been fun and eye opening learning about this tiny slice of the planet.
The plan is definitely to do metal shingles, while it may be more expensive and will be quite difficult (but I think any material on a dome is going to be hard!) it seems the most prudent choice. We'll lift some of the existing shingles in areas where we've seen tiny signs of water entry and see what's going on under there but just seeing all the nails coming through I feel like removing them all is going to make the dome swiss cheese! We'll see how we go, I'll for sure be updating this thread along the way.
I'm not so patiently waiting for the oodles of snow to melt off, another challenge of being east facing and having so much tree cover. But I am excited to learn how to live with the land and the seasons vs fight it or try to change or control it.