Black seems to get a strong initiative and two pawns for a piece in line B, which may be white's best try. In line A, white has to setly for equality in A2,3 or 4, because A1 seems good for black. Line D and 11.Be2 might require further analysis.
Upon overwhelming request, in algebraics:
(about the names of the variations, I thought it best to pinpoint certain tabiya positions and only then systematically name variations, so as to avoid lines called A12b2331, etc.)
1. e4 e5 2. Nf3 Nc6 3.
Bc4 Nf6 4. Ng5 Bc5 5. Nxf7 Bxf2+ 6. Kxf2 Nxe4+
7. Ke3 Qh4 8. g3 Nxg3 9. hxg3 Qd4+ 10. Kf3 d5 11. Rh4
(11. Be2 mysticknight's suggestion, which I have yet to look at.)
11... e4+ 12. Kg2 O-O 13. Nc3 (tabiya one, who knows a name?, Nc3 is variation A)
(B)13. Bb3 Rxf7 14. Qg1
(14. Rf4 Rxf4 15. gxf4 Be6 16. Nc3 unclear)
14... Qe5 15. Nc3 g5 =)
(C)13. Qh5 Rxf7 14. Qxh7+
(14. Bb3!?)
14... Kf8 15.Qh8+ Ke7 16. Rf4
(16. Bb3 Qf2+)
16... Rxf4 17. gxf4 dxc4 -/+)
(D)13. Rf4 dxc4 14. Qf1 Be6 15. Ng5 Bd5 16. Nc3 e3+ =)
(A ctd.)13... dxc4 14. Qh5 Ne7 (A1)15. Qxh7+
(A2)15. Nxe4 Bf5 16. Nfg5 h6
(16... Qd5!? 17. d3 cxd3 18. cxd3 h6 19. Nf3 Ng6 20. Rh1 unclear)
17. Nc3 Bg4 18. Nh3 Qf6 19. Rxg4 Qf1+ 20. Kh2 Rf2+ 21. Nxf2 Qxf2+ 22. Kh3 Qf1+ =)
(A3)15. b3 cxb3 16. Qxh7+
(16. axb3 Ng6 =)
(16. Ng5?? Qf2+)
16... Kxf7 17. Rxe4 Qd6 18. Rf4+
(18. axb3? Bf5 19. Rf4? Qxf4 -+)
18... Ke8 19. Qh5+ g6 20. Rxf8+ Kxf8 21. Qf3+ Kg8 22. axb3 Bd7 =)
(A4)15. Rxe4 Qf6 16. Rf4 Qc6+
(16... Qg6?! 17. Qxg6 Nxg6 18. Nh6+ gxh6 19. Rxc4 +=)
17. Kg1
(17. Rf3 Qe8 18. Nh6+ gxh6 19. Rxf8+ Qxf8 20. d3 cxd3 21.
Bxh6 Qf7 22. Qg5+ Qg6 23. Qxe7 Qxh6 24. Qd8+ Qf8 25. Qd5+
Qf7 26. cxd3 Qxd5+ 27. Nxd5 c6 28. Ne7+ Kf7 29. Nxc8 Rxc8
30. Rh1 Kg6 =)
17... Qb6+
(17... Qe8?! 18. Nh6+ gxh6 19. Qxe8 Rxe8 20. Rxc4 +=)
18. Kh2
(18. Rf2 Bf5 19. Nd5
(19. Ng5? Qxf2+)
19... Qxf2+
(19... Qc5? 20.Nf6+ gxf6 21. Nh6+)
20. Kxf2 Nxd5 21. Nh6+ gxh6 22. Kg1 Rae8 with decent compensation.)
18... Qg6 19.Qxg6 Nxg6 20. Nh6+ gxh6 21. Rxc4 Be6 = 22. Rxc7?? Rf2+
with a strong attack, e.g.: 23. Kg1 Raf8 24. Ne4 Rf1+ 25. Kh2 Bd5 26. d3
Bxe4 27. dxe4 R8f2+ 28. Kh3 Rh1+ 29. Kg4 Ne5#)
(A1 ctd.)15... Kxf7 16. Rxe4 Qf6 17. Rxc4 Bf5 18. Qh4
(18. Qh1 b5 19. Nxb5? Qe6 20. Rf4 Nd5 21. Rf3
(21. Rf2? Kg6 22. Kg1 Bd3 23. Qg2 Qe1+ -+)
21... Qe2+ 22. Kg1 Kg8 -/+)
18... g5 19. Qh5+ Kg7 20. Qe2
(20. Rxc7?? Bh3+ 21. Kxh3 Qf1+ 22. Kg4 Qf5#)
20... Rae8 And black has a strong initiative, e.g.: 21. Rxc7?? Bg4 22.Qe1 Bf3+
23. Kg1 Rh8 -+
This is the current state of the analysis. I haven't incorporated mysticknight's suggestion from post #154 from the original forum yet. What is a main and a side variation is a little arbitrary, but this is a start.