I live in CO. I'm gonna guess that the UV in the high Rockies is killing the plastic in your dome in short order. UV will also shorten the life of even a high grade cover like you have on your yurt. Since you rarely visit the yurt, how about considering covering the entire yurt with a large white tarp to protect it from UV degradation? Just cut a hole for the stove pipe if necessary, and snug the tarp tight to the yurt wall with a rope running circumferentially around the yurt. Like Mongolians do.
Another cheap solution if you have a UV problem would be to apply 3M 303 protectant to the plastic every time you visit the yurt.
As far as removing the yurts cap and covering the smoke hole with plywood, sure you could do that. Even if you have a double wall stove pipe exiting the roof ring, you'd still need to keep combustion in mind when you are using the stove.
To avoid using plywood up there, you could make a sheet tin 'china cap'. I made one for my yurt from sheet tin from Home Depot. The stove pipe pokes up through a hole in that and combustion isn't an issue. It holds in the heat. I might have ten bucks in the cap.
Good luck.
