What I get from it is that neither of them got their happy ending in reality -- instead, they got it on 'the moon', far-away on some distant plane, a possible alternate outcome that their hearts yearned for so much that even if it wouldn't manifest in real life, it at least could in memory, Frankensteined and cobbled together as it were.
In my head, what drove River to her actions late in life was her awareness that something was off with Johnny, that he was missing a chunk of his childhood experience with her. She was driven by the past, while Johnny's was taken away from him; and she wanted to restore it, for him to return to her the way he thought she did when they rekindled their relationship as adults. In the end, it feels like fulfilling Johnny's 'dying wish' was also a way to fulfill, perhaps, River's -- it was his way of apologizing to River and meeting her halfway, if not in life, then maybe beyond it. Even if doing so in real life was, ultimately, no longer possible. That alone wasn't enough to stop their souls from trying, whether their physical bodies would allow them or not.
