I think 6.dxe5?! is premature, but 6...dxe5 7.Nh4! looks like a good followup to me.
Compare: 1.e4 d6 2.d4 Nf6 3.Nc3 e5 4.Nf3 Nbd7 5.Bc4 Be7 6.O-O O-O is the typical position of the Improved Hanham variation. These days white usually plays 7.Re1 or 7.a4. An older idea for white is 7.Qe2 c6 8.Rd1 Qc7 9.a4 h6 10.dxe5 dxe5 11.Nh4! with advantage to white. This has been known since the 1970s, but fortunately for black either 7...exd4 or 8...exd4 or even 9...exd4 gives adequate counterplay, which is why masters switched to 7.Re1. The point of all that is, if white can arrange it then d4xe5 ...d6xe5 Nf3-h4! is exactly what white wants.
I consider the plan with ...h7-h6 and ...g7-g5 to be unsound. Nevertheless it's interesting. I looked in Van Rekom/Jansen (2008) The Black Lion. With the 5...h6 move order they analyze only 7.Bxf7+, on pages 165-172. It seems they mostly prefer the 5...Be7 move order. I also looked in the ChessBase database and found two relevant games. These are not perfectly played, but you can check them with an engine just as easily as I can.
(1) Van Rekom/Jansen, pages 112-115 : 1.e4 d6 2.d4 Nf6 3.Nc3 e5 4.Nf3 Nbd7 5.Bc4 Be7 6.O-O h6 7.a4 c6 8.dxe5 dxe5 9.Be3 (a) Qc7?! (b) 10.Nh4! g6 (c) 11.f4! exf4 12.Bxf4 Ne5?! (d) 13.Nf3?? Qb6+ 14.Qd4?? (0:1) R.Morlock - M.Bergmann, Steinhaldenfield 2001
(2) database.chessbase.com : 1.e4 e5 2.Nf3 d6 3.d4 Nf6 4.Nc3 Nbd7 5.Bc4 h6 6.dxe5 dxe5 7.Be3 c6 8.a4 Qc7 9.O-O Be7 10.Nh4 (e) Nc5 (f) 11.Nf5 Bxf5 12.exf5 O-O 13.Qf3 Rad8 14.Qh3 Kh7 15.g4 Nfe4 (1/2, 54) P.Zagrapan (2194) - T.Liscak (2028), SVK-chT2 2003-04
(3) database.chessbase.com : 1.d4 d6 2.e4 Nf6 3.Nc3 e5 4.Nf3 Nbd7 5.Bc4 h6 6.dxe5 dxe5 7.Nh4 c6 (g) 8.a4 a5 (h) 9.O-O Qc7 10.Kh1 Nc5 11.f4 Be6 12.Qe2 Bxc4 13.Qxc4 Ne6 14.f5 Nc5 15.Be3 b6 16.h3 Be7 17.Nf3 Rc8 18.g4 Ncd7 19.Rad1 Bc5 20.Bc1 Rb8 (1:0, 38) Z.Runic (2427) - A.Jurkovic (2330), Zagreb op-A 2010
- It seems white could play 9.Nh4! right away (not mentioned in the book), before black can play their recommended improvement 9...g5. After 9.Nh4! Nc5 (idea ...Bc8xNf5) 10.Qe2 is better than 10.Be3.
- They analyze 9...g5!, which also prevents 10.Nh4.
- About 10...g6 they say "The usual reply, which keeps the white knight from f5". This sort of note is why you shouldn't trust books by non-masters. Then they analyze 10...Nb6! 11.Ba2 (11.Bb3, not mentioned, is a tiny improvement) Ng4 12.a5 Na4 leading to equality.
- They actually spend two pages analyzing the complications after 12...Qb6+. I won't get into it, because 10...g6 is just a bad move, but I will point out 12...Qb6+ 13.Kh1 g5 14.e5! "White obtains a crushing attack ..."
- After 10.Nh4 it's the same position as the Morlock - Bergmann game, where 10...g6 was played and 10...Nb6 was analyzed.
- 10...Nc5 is logical, covering f5.
- Certainly not 7...Nxe4? 8.Bxf7+. The only try to "punish" 7.Nh4 is 7...g6 8.Qe2 Be7 9.a4 Nxe4? 10.Nxg6 Nxc3 (a typical desperado which is also quite common in the Sicilian) 11.Nxh8! Nxe2 12.Bxf7+ Kf8 13.Bxh6#. Of course black doesn't have to get mated, but 9...Nxe4? just loses.
- Again not 8...Nxe4?! 9.Bxf7+ Kxf7 10.Qh5+ Kg8 11.Nxe4. But there are a bunch of moves which are close to equal, possibly a bit better for white: 8...Bb4, 8...Bc5, 8...Qa5, 8...Qc7. e.g. 8...Qc7 9.Qe2 Nc5 10.O-O Ne6 11.Qd3 Nc5 12.Qf3 Bg4 13.Qg3 Be6 14.Bxe6 Nxe6 15.Be3 Bb4=.
Engine analyses don't help me understand the plans in these positions. Anyone have a solid grasp of the lines here, especially those without short castling for Black?