First of all this is just a Hanstein Gambit - 3.Nf3 g5 4.Bc4 Bg7 5.O-O d6 6.d4 h6 7.c3 Ne7.
It has been a few years since I looked at this systemetically, so my thoughts might be outdated.

I like 6...Nc6 better than 6...h6, because White might take benefit with 7.g3. It's not that clear though.

Another point is that I'm not sure if 7...Ne7 is better than 7...Nc6. I think 8.g3 Bh3! 9.gxf4 Bxf1 10.Rxf1 Qd7! good for Black, Nokes-Sarapu, NZDch 1979. On this site other 8th moves have been analyzed by FM Bücker and TalJechin.
In general I think that White's g2-g3 should be answered with Alapin's Bc8-h3. What you call continued Kingside aggression with ...g4 and ...f3 is not aggression at all. White usually can maintain his centre, keep his King safe and eventually sac a Knight on f3. That also seems to be true in case of 6...h6 7.c3 Ne7 8.g3 g4 9.Nh4 f3 10.Nxf3 gxf3 11.Bxf7+ Kxf7 12.Qxf3+ and 10.Bf4 with the idea of x.h3 h5 and y.Nd2, in order to sac the Queen's Knight. I would not like defending Black.

After 6...h6 7.c3 Ne7 8.g3 Black is a move further away from castling Queenside, so 8...Bh3 might not be optimal either.
8...d5 isn't clearly refuted (yet?) but I would not like to play with a centralized King in such an open position.
That leaves the critical 8...Ng6.

But remember - if 8...Ng6 is good for Black indeed there is still 7.g3.