An interesting thread! I've been an ardent 1. Nf3 player for some years now and the d3 line is something I've toyed around with after seeing people get hacked up in main line Leningrads. I'm a bit surprised by some of the comments that Black should just be ok without a worry. Maybe a playable position is achievable and d3 isnt the most active move on appearances but its very logical and dangerous immediately trying to open things up. I don't want to give too much away but I have a few thoughts about 2. ... Nc6 which seems the most ambitious move.
After 2. ... Nc6 it seems 3. e4 just isn't very good - I was unaware of Kindermann's suggestion 3. d4 and prepared it a year or two ago for a match using material from SOS and a game I found on CB of my opponents. He slow played a line that's supposed to be inferior for Black to sucker me in before uncorking a novelty he'd had lined up for a while. I can't remember exactly which move was the novelty but I'm happy sharing what I can remember of the game seeing as I dont intend to ever play 3. e4 again... 3. e4 e5 4. Nc3 Nf6 5. exf5 d5 6. d4 exd4 7. Nxd4 Nxd4 8. Qxd4 Bxf5 9. Bg5 It looks to me like Black has got a vastly improved version of the lines with d6 and in particular is doing well due to 10. Bxf6 Qxf6 11. Qf6 gf 12. Rc1 Bg6 13. Nxd5 0-0-0! 14. Nxc7 Kb8 and good luck trying to defend this position with White...
However although I think Kindermann is a little overly pessimistic about Black's position and White must find some good moves 3. d4 is still challenging. 3. ... e6 was my initial idea upon and at first I thought Black was just ok but now I think this was too hasty.
A/ 4. d5 looks artificial and after 4. ... exd5 5. Qxd5 Nf6! 6. Qxf5 d5 7. Qd3, a position mentioned earlier in the thread, Black seems to have good compensation. I strongly disagree that it's difficult to get an advantage with Black against the BDG and I'll happily take on anyone willing to give me a pawn on move 2 for nebulous compensation, but not with my queen on the stupid d3/d6
B/ 4. c4 seems very natural, going into a kind of Nimzo/Queen's/Bogo indian position with certain pros and cons. As White has played d3-d4 and Black has f5 in which is generally useful to fight for e4, the key square in these positions, and Nc6 it seems souped up for Black. However although the move Nc6 is 'free of charge' it may not be well placed and open to a quick d5.
I haven't looked in detail at 4. ... Qe7 but I really dont understand such a move. Against d5 and planless play by White it does look an appealing and creative attempt that I'd not seen before but if White just ignores it and carries on with Nc3 and g3 what is the queen doing here? I would rather have natural harmony amongst my pieces when available than go into a strange position for the sake of it. Moving the queen to a square where it blocks the bishop going to b4 and fighting for e4 cannot be right to me...
4. ... Nf6 seems like a much better move, particularly as 5. d5 Bb4+ doesn't work so the first danger is over for Black. After 5. Nc3 Bb4 the position is still complex with chances for both sides and I think that Black isn't doing badly but White surely isn't out of resources trying for the advantage either.
For me its a simple pragmatic choice, there are a lot of decent Black openings which lead to equal or very close to equal positions with perfect play and this is unavoidable but there is still lots of fight and this is just like any of those. If I have to choose between playing this which is similar to a lot of other d4/Nf3/c4 indian positions that I get frequently and have experience in and having to learn the whole of the Leningrad Dutch and then succesfuly remember all the theory for the one game I get in it whenever the moon happens to be blue I'll take the former. Maybe there's something stronger than both these lines for White anyway...