I agree with most of what you said though I have no personal problem with him doing earlier songs as he says during his show that he joined in 1974, but he also acknowledges that PEF and TIE are from 1971. But I also think he's verbally tried to portray himself as being an integral part of the band from the beginning, which is not quite accurate as you said. Randy and Bernie actually had a lot more experience in the music business than Don and Glenn when the Eagles started. The most spontaneous DF performance I have ever seen was when he did a small show at a center for people with brain injuries (link below). Apparently he did acoustic solo versions of "Desperado" and "Best of My Love." Wish the entire songs were available online as I've never heard him do either of those songs anywhere else.
https://www.youtube.com/watch?v=4wxLXtX-OD8