Depending on whether it's butterflied away or not, the faces on the mountain (or anywhere else some sort of monument is created) will be somewhat different. TR is a must, as he's the man that brought the US to glory after two humiliating defeats. I can imagine Mahan maybe getting up there (prior to TR's administration, Alfred Mahan (1889-1897) was considered the US's greatest president), or if it happens late enough, one of La Follete. I think Washington would get on as well, seeing as he is considered the father of both the US as well as the former Confederacy, so you can interpret it as a reason to full unification.
It always was a pet theory of mine that Washington would get a great(er) status again (not that he necessarily lost it) in TTL due to being a symbol of unity during the Revolution, and the country looking back to such a time for such heroes and unity of purpose.