I am a big advocate of building legit shit, and building it legit makes certain that will be there year after year.
If you know the forester, there may be an opportunity to build a structure as part of their logging operations. If so, that would be awesome, but the hut may have to be destroyed when logging operations conclude.
The guy you really want to know is the parks land manager for the area.... this helps for a few reasons. If he likes you, he may look the other way and if him and his crew stumble upon it, knowing you they may be less like to destroy it.
2 of the best ways to do this above bar are;
Find some one who has a recreational tenure on the land (heli ski company as an example) they can usually build limited structures without much headache. its a good partnership, especially for remote tenures.. the heli guys love knowing there is a warming hut that they can set down at incase shit goes sideways.
or
Get the mineral rights to the land. this is probably the easiest, if you dont have some good connections in the area. With mineral rights, you can get away with a lot of things.. you just need a prospectors license and to keep your claim current.... if you go this way, you need to get sluice box and a shovel, and keep it at the cabin.