Apologies for lack of updates- I haven't been doing quite as much with the online articles since taking up my new job (although I have joined Exeter Chess Club).
The latest update on the King's Gambit has involved increasing the amount of verbal explanation for the early moves of the game in the annotated games sections, while I have had a closer look at the lines discussed at Chess-Brabo.
The latest articles are here:
3.Nf3 d6 and h6
Vienna Gambit lines
"Vienna Gambit lines" refers to the Hamppe-Allgaier and Pierce Gambits that normally arise from 1.e4 e5 2.Nc3 Nc6 3.f4 exf4 4.Nf3 g5 5.h4 and 5.d4 respectively. The King's Gambit move-order to those lines is typically 1.e4 e5 2.f4 exf4 3.Nf3 g5 4.Nc3 Nc6 5.h4 or 5.d4, while 5.g3 is most consistent with a Quaade Gambit-based repertoire.
In the Fischer Defence, 1.e4 e5 2.f4 exf4 3.Nf3 d6, Black intends to play 4...g5 but without allowing the white knight on f3 access to e5, and thus preventing the Kieseritzky Gambit (3...g5 4.h4 g4 5.Ne5).
White can continue with 4.Bc4, which normally leads to a Hanstein Gambit after 4...h6! intending 5...g5 (rather than the immediate 4...g5?! which is met by 5.h4 and if 5...g4 6.Ng5 and White's knight and bishop both hit f7).
Instead 4.d4 g5 5.h4 g4 6.Ng1 is the traditional main line but I don't think White gets enough development there to give much compensation for the pawn.
I am inclined to agree with John Shaw that continuing in Quaade Gambit style with 5.Nc3 with g2-g3 to follow. Then "brabo" recommends 5...h6, which is at least as good as anything else that Black has. 6.g3 Bd7!? is an interesting suggestion of his, not allowing White the standard development plan of Be3, Qd2 and 0-0-0, and White probably does best to switch plans with 7.Bc4 and 8.0-0. While I don't quite agree that "it is very difficult for White to keep the balance", Black certainly doesn't stand worse. Instead, 6...fxg3 7.hxg3 allows Black to flick in ...Nf6-g4, whereupon White can allow the exchange of knight for bishop by playing Be3, Qd2 and 0-0-0, or meet ...Nf6-g4 with Be3-g1, which leaves White's pieces bottled up on the first rank but White still appears to get reasonable compensation for the pawn.
This is also relevant to the Becker Defence, 3...h6, which aims to avoid the Kieseritzky Gambit, since after reinforcing the g5-pawn, Black does not have to meet h2-h4 with ...g5-g4, and the interesting idea 4.b3, discouraging 4...g5, is well met by 4...d5 (or 4...Nf6- Shaw).
White again has the option of the Hanstein Gambit with 4.Bc4, but probably best is the Quaade Gambit style line 4.d4 g5 5.Nc3, and then Black's best is probably 5...d6, leading to the same position as I discussed earlier under the Fischer Defence.
This certainly appears to be one of the most critical positions in the early ...g5 lines of the King's Gambit at the moment. White's better development counterbalances Black's extra pawn.
So, in conclusion, both 3...d6 and 3...h6 are probably about equal in value with 3...g5, though they narrow down Black's good options against the Quaade Gambit approach since if White plays 3...g5 4.Nc3 then Black has other good options besides playing 4...d6 5.d4 h6. One significant advantage of 3...d6, however, is that it tempts White into the line 4.d4 g5 5.h4 g4 6.Ng1, which is inferior to the Kieseritzky Gambit with 3...g5 4.h4 g4 5.Ne5.