Buddy had some land with an easement through Park land. They where really bad to deal with, constantly sending out the rooky Rangers to lock the gates, put chains across the roads or just sit there in a truck and stop us from driving the easement. Since they didn't have badges and where not allowed to arrest us when we ignored them, they would call the Sheriff on us pretty often. Even had them come after us in a helicopter. Since the easement was legal, and the owner of the land was heavily into politics and enjoyed fighting with the Park, nothing ever happened and he sued them a lot, and won every time. They also sent the Game Wardens after us, which just kept us legal and eventually we got to know them pretty good and they would even let us know where they saw a nice buck that we had permission to be.
In my experience, the Park will bluff, lie and make up stuff to get their way, or just bully neighbors. They hundreds of millions of dollars to buy more land, and in my experience, harassing neighboring land owners is the easiest way to get them to sell them their land. There is no reason to be afraid of the Park, but you have to know the law and understand they they are bluffing a lot of the time.
Having said that, if you do break the law, expect them to use everything that they have to punish you. They can be extremely vindictive.
Not knowing what you are dealing with, taking the house apart by hand sounds like a reasonable project. Just have lots of dumpsters on hand and keep the work site spotless. Bid it accordingly and add enough to deal with the BS factor. I would also have payment schedules based on how much progress you made and not wait until it's done. You do not know what the Park, or a Park friendly government agency might get involved in this and shut it down for a study of some kind, or permanently.
One of the most ridiculous studies that my friend had to do was prove that a certain type of salamander wasn't affected by using his easement. Turned out that the salamander in question didn't exist in that area of the hills and it was all just a way of wasting money to harass my friend. He sued, won, and I think he got $50,000 for that one. We did other studies for snakes and birds that ended with similar results. And I wont even go into what happened when we started trimming trees along the easement!!!!!