According to you 6.Bd3 c5 7.Be3 is inferior to 6.Bg5. As the latter leads to equality after Black's best play (imo 6.Bg5 Be7 7.Qd2 Nbd7 is critical, but we'll save that for another time), the first will lead to a Black advantage following your logic.
What's more, you admit that this line is an inferior version of the Alapin, which again is equal after Black's best play. This is another sign that 6.Bd3 c5 7.Be3 is better for Black.
Finally you gave as an example Abbasifar (2353) - Tehrani (2173) , Teheran 14th Fajr Open, 2006, 1-0/25. Black had a won position around move 15.

So your only defence of 6.Bd3 c5 7.Be3 is "plenty of Black players do not know anything about this theory." In other words, you recommend a line for White that can be refuted if Black finds the best 10 moves or so, but speculate that Black won't. That's called hope chess. The only way to escape this conclusion is to find a major improvement on the abovementioned game - for White. I would welcome that, as I find Studier's plan (for other readers: Bd3, Qh4, Bg5, Ne5 with mate to follow) very appealing.

That's up to you to tell us. Regarding that Abbasifar (2353) - Tehrani (2173) , Teheran 14th Fajr Open, 2006, 1-0/25, why don't you try to find some good moves for Black? Just one place to start is Black's 15...Ne5? I am sure that an attacking player like you can find a good move for Black here.

Gambit wrote on 03/03/09 at 03:11:54:

You nicely gave the answer in the French thread "Gambit on the 3rd move."  It does not mean according to you - and I agree - that this move order provides sufficient compensation. Thank you.

That's not an answer to my previous post. So I feel free to conclude that (BDG) 5...e6 6.Bd3 c5 7.Be3 leads to nothing, exactly because it transposes to an inferior form of the Alapin.

What is exactly the difference with  1.e4 e6 2.d4 d5 3.Be3 dxe4 4.Nc3 Nf6 5.f3 exf3 6.Nxf3 c5 7.Bd3  ? That 7.Bd3 is an inferior move here? Then 6.Bd3 is inferior against the Euwe. I would have thought that a BDG-expert like you would have thought of this himself.

This game does not address my second point. It's in fact an Alapin Gambit (1.e4 e6 2.d4 d5 3.Be3) which easily can be improved upon by Black.

There are two problems with 6.Bd3:
1) 6...c5.
2) I want to play this line via 1.e4 e6 2.d4 d5 3.Nc3 Nf6 4.Bg5 dxe4 5.f3 exf3 6.Nxf3.

To quote what drkodos once said about another of your threads: 

'This thread is like a herpes.

No telling when it will flare up again.'

I checked Internet Chess Club today for Birchbeer's games. All of the games were played at 2 14, 5 15, 10 0, or similar time controls. This means that the increment gave extra time for the computer to find a move.

Tim McGrew once told me that Birchbeer was actually a master that left once ICC started requiring computers (C) to be labelled so. According to Tim, Birchbeer used an early version of Fritz to help him.
The last of Birchbeer's games are from 1999.

He has not been heard of since.