Although I'm 800 Elo below the OP so he's scarcely in need of approval from a woodpusher of my kidney, I've been a lifelong KG player and am the sort of obsessive chap to have bought all the books. For whatever it's worth, I agree with his analysis having thought awhile and gone hunting through the literature. Can't fault it. The 3..., Qh4+ then 6. Be2 and so on line is given in Shaw as his recommendation for White.
I suspect that many a KG player seeing this gambit for the first time will bale out with 3. Nc3. I know that I for one would have. I suspect that's an okay if unambitious move too.
I've started seriously studying the little-known Panteldakis Countergambit, which I find to be a very interesting practical option at least for blitz games.
That said, in more serious games, I believe Black should probably go for more critical lines.
This variation seems to have a provocative, annoying effect on King's Gambit players, and there's a good chance they’re not well prepared for it.
I consider it an easy option to study with Black, unlike other more critical lines like, for example, the Falkbeer Countergambit.
There are two main lines for Black in the Panteldakis: 3...Qe7, which seems to be the strongest and most ambitious option though also a bit more complex
and the simpler choice of giving a check on h4, then retreating the queen to e7 after White plays g3.
In that second line, queens are usually traded and Black tends to equalize quickly.
That said, White does have an annoying sideline with Be2 to block the check hardly anyone plays it, but it’s not the end of the world either.