What I got out of it honestly was just the madness that can come about from such sheer and intense isolation. Even in the scenes where they are seeming to connect with one another instead they just end up getting locked into a grand delusion together, almost feeding on each other's mental breakdown.

In the end I don't actually believe anything supernatural was going o rather that just serves as a good visual for how the characters were feeling in their states of madness. I think the end shot really highlights this as the two are shown in the state that they are in.

I think you pretty much nailed the Mt. Rushmore but I'd throw in Bride of Frankenstein as well.