Firstly, I said it was my opinion. I am not an all-knowing oracle, and my opinion is also that openings like the latvian are playable, where most GMs would argue. And let's not forget that some masters have called the Dragon unsound too - it's their opinion, not a fact.
Now, onto some analysis. The first point to note here is that black, according to your "prepared player" statement, has to decline all these gambits. Already I'd say white has a psychological advantage if he can offer one of these "insane amateur gambits" (Korchnoi probably would be quite unhappy at being called an amateur) and black can't afford to accept.
Okay, I'm unsure about your line against 2.h3 - 2...Nf6 3.g4 Nf6? I dont think this is possible. If you mean instead 3...Nc6, then I'd assess 4.d5 Ne5 5.Nf3 as at least equal - white can go q-side and the advanced k-side pawns will facilitate an attack, while in other lines the d5 pawn can be quite cramping. Maybe 5...g5 Ne4 6.Nc3 isn't so bad for white either - I'd rather be white in either of these positions.
Secondly to your line against 2.Qd3, I dont have to go too far. After 2...d5 3.g4 g6, white shouldn't be even considering 4.gxf5 Bxf5 after his opening. Instead, 4.Nc3! seems the strongest continuation. I'm playing a gambit here, not a dull positional opening - if white plays something like g4 then switches to quiet play, he will indeed be worse. However, 4.Nc3 and then black, unless he wants to go back into the accepted gambit lines with 4...fxg4 (on which, either 5.h3 or 5.Bf4 seem to offer white more than enough compensation), or what else? 4...Nc6 or 4...Bg7 can both be met by 5.Bf4, where I prefer white's chances.
Finally, 2.g4 I did say to be playable, but not the best of these lines. Your line for black is the most commonly played, but again I like white's postion, even if the g-file hasn't been successfully opened.
The dutch was intended as an aggressive, counter-attacking opening. But when there are such a range of clearly playable gambit lines where black does better to turn it down, and white still has his attacking chances - this I dont consider to be sound. I'm not saying that it means it's unplayable, it's just an opinion. There's no fully standardized definition of "sound" and "unsound", and it depends as much on personal preference. Try telling Johnny Hector (or maybe our very own Tony Kosten!) that the latvian is unsound, I doubt you'll get them to agree. The Hungarian master Kadas would never admit to 1.h4 being unsound. I'm not the only person to think the dutch is unsound, and you're not the only person to disagree with that statement.
And playing one correspondence game in the line will not change the assessment - I'm certain if I did beat you in a miniature you'd still claim that the dutch was fully sound, and if I lost quickly I'd still think the dutch a rotten opening. C'est la vie!
Regards,
Craig