I wish I had taken a look at this thread as I was preparing some recent analysis of this line of the Two Knights:
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.d4 exd4 5.e5 Ng4
http://kenilworthian.blogspot.com/2013/04/the-two-knights-anti-modern.html
http://www.kenilworthchessclub.org/games/java/2013/C55-Ng4.htm
where I analyze 6.O-O Be7(!)  which can basically transpose to your line if White plays e5.  I think your idea has merit and might work really well with the repertoire I present.  I will have to take a closer look at it.

I think it puts the cart before the horse to call 5...Nxe4 the "Anti-Max Lange" (as described in the pgn notes below), though I know one recent book calls it that.  5...Nxe4 is simply the main line after 5.0-0, and objectively, it is fairly obviously the best move.   Nobody would play 5...Bc5 unless they were extremely well prepared (or in corr chess and looking for a hard fight), but if one is better prepared (or better equipped, in case of corr chess), one can win that way.  I would not consider 5...Be7 for a second, though what has been said about it here is interesting.

Yes, I think micawber's line with Rd1 is looking good for White.

In the 9. Nh6+ line, 1. ...c6 may be an improvement for Black.  But, ignoring that,  yes, White stands better in your lines.

In practice, none of this may matter for OTB play at my level but it helps to get the lay of the land. 

micawber's line looks critical to me as well. After 17.Rd1 in his line, Black also has 17...Bxc3!? 18.Rxd8 Rbxd8, when Black has two rooks for the queen, but the knight on a1 is not looking particularly happy. I only have an old version of Fritz available right now, and it gives this as equal, but I would prefer White - Black's queenside looks vulnerable, and Black's knight is not easy to get back into play.

Another line I think is critical is 9.Nh6+ gxh6 10.Qxe4 Ne5 and now not 11.Nc3, but 11.Bxh6! Nxc4 12.Qxc4 and now:

a) 12...Bxb2 13.Nc3 Qf6 14.Qb4 Qxh6 15.Qxb2. I think White has excellent compensation here; Black's kingside is damaged, and he is struggling to complete his development on the queenside.

b) 12...d5 13.Qd3! Bxb2 (Fritz gives 13...Re8 14.Nc3 c6 as equal, but it looks slightly better for White to me due to Black's damaged kingside) 14.Nc3 Qf6 15.Bxf8 Qxc3 (15...Bxc3 16.Be7! Qe5 17.Rab1) 16.Rab1 Kxf8 17.Qb5. Black's b2-bishop is lost, so White will emerge with an exchange for a pawn.

Small note:  on 6. e5, 6...d5 isn't playable.

I notice ECO thinking that 6. Re1 d6 7. Nxd4 0-0 8. Nc3 compares unfavorably for White to having h3 in instead of Re1 (as in e.g. Spassky-Hort).

edit:  and in the Bilguer version with Bf4, 8...Re8 seems non-best ...

The line you point out can cause some problems for Black.  

Also, the main line that I give is not as robust as I thought when I first did this analysis back in 2008.  Without any improvements its value may just be the surprise factor.

Thanks for the feedback!

This is from some "fun" analysis I did back in 2008.  Is 5. ... Be7 playable?