A fourth union of Elves and Men??

[Voralphion]

However, Tolkien's exact words were that there were three unions of the Eldar and the Edain. Now, the Eldar were originally the name of all Elves, but then only those who made the Great Journey to Valinor were known as Eldar afterwards

Actually the Eldar were all those who started the journey not just those who finished it. The only elves who were not counted as eldar were the avari. The teleri who never made it to Valinor were still Eldar, but they were Moriquendi and Calaquendi. Even the Nandor who turned from the journey before entering Beleriand were counted as Eldar.