One of the main assets when playing the DDG as White is Black's bad bishop, blocked by e6. Hence, it is difficult to reach a similar reversed position where White had played e3. Anyway, in some openings White might just do it, like in this (almost) imaginary game:
1. d4 d5 2. e3 (Queen's Pawn: Stonewall Attack) e5 3. dxe5 c5 4. Nf3 f6 5. Bb5+ Nc6 6. Bxc6+ bxc6 7. O-O Qc7 8. exf6 Nxf6 9. Nc3 Bd6 10. b3 O-O 11. Bb2 Ne4 12. Re1 Bg4 13. h3 Bxf3 14. gxf3 Ng5 15. f4 Bxf4! 16. exf4 Qxf4 17. Kg2 Qxf2+ 18. Kh1 Nxh3 (18... Rf3!) 19. Rf1 Qg3 20. Rxf8+ Rxf8 21. Ne4 Nf2+ 22. Nxf2 Rxf2 23. Qxd5+ cxd5 24. Rg1 Qh3# 0-1.
After 12... Bg4, the game follows Montenero - Kasparov Champion, 1996, but reversed -- and Black is even one tempo up!
7. Be2 f6 8. exf6 Nxf6 9. O-O Bd6 10. Kh1 Bc7 11. Re1 O-O 12. h3 Bf5 13. Nbd2 Qd7 14. Nh2 Bxh3 15. gxh3 Qxh3 16. Nf1 Ne4 17. Be3 Rxf2 0-1, Anonymous - Heikkinen, Zone 1996.
The position of the diagram is a pure DDG Reversed: 1. d4 d5 2. c4 e6 3. e4 dxe4 4. Nc3 c5 5. d5 exd5 6. cxd5 Nf6, but Black is one tempo down. Nevertheless, even Tartakower played this variation in a number of games! Incidentally, the AC-G was introduced in the same year 1881 as the BDG. It became famous after the game Lasker - Albin, New York 1893.
Pitt has a collection of over 470 Albin Counter-Gambit games.