How to deal with the Cochrane Gambit [fen ""]

 1. e4 e5 2. Nf3 Nf6 3. Nxe5 d6 4. Nxf7 ?!


I'm pretty sure the Cochrane Gambit isn't correct. However, I find it difficult to defend against, as some "natural" moves don't seem to work. Can you give some advice how to deal with it? Further, I guess it might be a surprise weapon in a blitz game, so have some of you tried it out?
The Cochrane Gambit sacrifies his Knight for a few things:


He sacrifies the Knight for 2 pawns
After Kxf7, Black loses castling rights and is dangerously in the
center.
Blacks King-side is basically destroyed with only the g and h pawns
and it is not easy to find the best square for the Black King. 
Usually White will check with the Bishop with Bf4 and if Black
blocks with Be3, then White should just exchange bishops and bring
the black king further into the center making it harder to castle
manually.
White wants to build a strong pawn center by pushing his pawns
especially on the king-side. For example, White wants to develop his strong pawn center by pushing d4, f4, e5 and further fortify his strength in the center with Nc3 and Bd3 or Bf4.


With the above said, I think Black's goal should be to neutralize White's strong pawn center. In the Kramnik-Topalov game, I think Kramnik made a good move with 5...c5 to challenge the d4 square. From here White has to chose between playing 6. f4 followed by 7. e5 trying to break Blacks position, but in this case White's Bishop on c1 is not playing. Topalov instead played 6. Bf4+ to not lose any tempo and 6...Be6 is basically forced and after the exchange of Bishops, Black's King is more brought deeper into the center.

Some popular replies for Black after 5. Nxf7 Kxf7 6. d4 could be: 


c5
g6 
c6
Qe8
Be7


Lets look at the c5 first:

[FEN ""]
1. e4 e5 2. Nf3 Nf6 3. Nxe5 d6 4. Nxf7 Kxf7 5. d4 c5


White's most popular reply is 6. dxc5, followed by 6...Qa5+ 7. Nc3 Qxc5 8. Be3 and White maintains his the initiative.

Now onto c6:

[FEN ""]
1. e4 e5 2. Nf3 Nf6 3. Nxe5 d6 4. Nxf7 Kxf7 5. d4 Be7 6. Nc3 c6


Usually with 5...Be7, Black wants to try to castle manually and White continues development with 6. Nc3. After 6...Re8, Black is in trouble after Bf4+, so instead 6...c6 with the plan of playing d5 later. After 7...d5, it might continue 8. exd5 cxd5 9. Nxd5 Nxd5 10. Qh5+ Kf8 11. Bxd5 Qe8. I would say White is better here because his Black's King is still weak and he has 3 pawns for the Knight

Regarding g6:

[FEN ""]
1. e4 e5 2. Nf3 Nf6 3. Nxe5 d6 4. Nxf7 Kxf7 5. d4 g6


g6 might be Black's most popular reply. After 6. Nc3 Kg7 7. Be2 d5 8. e5 Ne4 9. Nxe4 dxe4 10. O-O Nc6 11. Be3 h5 12. f3 exf3 13. Rxf3 Be6 14. c4. Even with this, White still has an advantage.

Last, Qe8:

[FEN ""]
1. e4 e5 2. Nf3 Nf6 3. Nxe5 d6 4. Nxf7 Kxf7 5. d4 Qe8


Here Black threatens e4. It usually continues: 6. Nc3 g6 7. Bd3 Kg7 8. O-O Nc6 9. Bd3 Nc6 10. Be3 Nb4. White may panic here because of the attack on the White-Squared Bishop, but instead of panicking, White should play 11. h3 Nxd3 12. Qxd3 Rg8. Black wants to play Kh8, so White should go for the attack with e5. Black is very disorganized and in a positional disadvantage.

In a nutshell, I believe breaking White's center as Kramnik did is the best possible way to either draw or defeat the Cochrane Gambit