So, your family owns the old farm field you climb up the side of to the top of the ridge where the big, solitary tree is and at the top of the climb is a dirt road which the trail follows for a little while? I love the view from there back to the humps.
Since the Apple house shelter has been removed, having a "secret shelter" up on top of that hill would be great. Since the FS only has an easement for the AT on your land, I don't see where having an unmarked side trail to your little shelter would be a problem. And if you did keep the shelter secret, being only known in the hiker guides or word of mouth, the chances of the local kids learning about it is greatly reduced, especially if it is a stiff hike up that hill to get to it.
I belive there are rules in place to allow public access to your land which still protects you, often this is done to allow hunting and hiking on private land.
Tent platforms are simple wood platforms rised off the ground. This is usually done if the area is uneven or rocky and making good tent sites isn't practical. You could start with a platform and eventually add walls and a roof. A friend of mine built a tent platform on some property he owned and eventually built a nice litte cabin around it.
Would this be the view from the top of that field?
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