I agree with all your other points, but I think this one doesn't hold up.(3) There are narrative issues from a conceptual standpoint (without going into the obvious stuff, like the Starkiller). I think the whole "Luke is missing" angle just doesn't work. We're not given a good reason for it, nor is there any urgency to the mission to find him, especially when the characters are sidetracked by other things throughout the film. Simply put, we don't understand why all of the sudden Luke is needed right this second, given that the good guys seem to be blowing through hundreds of stormtroopers and besting dark siders without him. It doesn't help when the whole "mystery" of the movie is solved because R2 just randomly decides to "wake up" at the end and present the portion of the map where Luke is hiding.
Reason: He stopped training more Jedi after his failure with Kylo. The Dark Side (i.e. Snoke) want to find him and kill him.
Urgency: Kylo and Snoke are trying to find and kill him. Good guys want to find him first. Also, he's their friend, so they miss him.
As for R2 just randomly waking up, I can only speculate. I assume Luke has his own plans and wanted R2 to wake up at that exact time so they could find him. It would explain the brief vision Rey saw of Luke putting his robotic hand on R2 (vision of the past?).
Actually, just on that, what was the scene immediately preceding R2 waking up? If the theory is true, maybe the film makers hinted at R2's wakeup trigger in their editing?