I have to agree the groundwork for a converegence just isn't there. One of the biggest points people use in favor of a merged timeline scenario is the ceremonial prayer from the Subdued Ceremony memory, and while it's easy to want to stretch that into references of all three timelines, it could...
The official timeline doesn't claim BotW is at the end of all three, just that it's at the end of one of them but the decision on which has not been made. It could be they are leaving it up to the players to decide, or maybe eventually they will give it a placement.
Answering the question, a...