A from-the-beginning where Shinji doesn't immediately follow the letter? A super positive. Amusing escalation of methods to drag Shinji to Tokyo-3? Brilliant.
However, what is the timeline of these events? As far as I can recall, Shinji came immediately upon seeing the letter, sending him right to the Angel as it arrives. Here, we are already delayed by the initial letter's return, another letter, & now the VTOL trip. "According to canon," the Angel would have destroyed the world already - by a week. Or does Gendo already account for this, even though he seemed surprised?
It would be nice to at least mention Asuka. Misato was with her for a couple years, right? Also, for my clarification, was Rei already injured at the time NERV sent the letter? The hunt seems rather arbitrary without those details (although the commanders wouldn't care). He is third for a reason....
As an aside, it is rational for Misato or anyone else, like the Bridge Bunnies, to wonder why the Third Child was never brought in earlier? Rei & Asuka were there since NERV's creation, right? Or was it mentioned that they (whoever they may be) found out days before the Angel attack (from our perspective)?