Thanks for the great analysis and discussion.
Mendenhall and Nugget Falls are not within a National Park - it's part of the Tongass National Forest. We checked LAANC and B4YOUFLY and got an all-clear. We spoke to the park rangers, and they told us where we could fly (beach by Nugget Falls). There's not a lot of information available about this area, and you really need to dig into the sectional charts to see that it is uncontrolled airspace.
However, I would add that the Forest Rangers made it quite clear not to fly over people or wildlife.