So it seems that there are 3 critical moves: Bf6, with the threat of Bxa3, Nf4, threatening Nd3, and Nf6, maintaining the tension.
Martin vs The world Analysis thread

JARP, currently studying your Bf6 and it is a brilliant move. If he takes our Knight with the pawn, then we take his Knight with our Bishop, and we are attacking his Queen and Rook at the same time!
Not only that, but he would capture back our Bishop with his Bishop and put his Bishop at its weakest square on the entire board!
Furthermore (haven't studied it in detail for all ramifications), if it goes through as expected, it would be our move next after his Bishop takes ours, and we then take that pawn on d5, and we are ready to trade Queens: Up an exchange, and a pawn to boot!

Hang on, because there is still one thing I'm confused about. After moving one square, do the DB's HAVE to turn if it is possible, or can they stay put? In simpler words, would Bd2 be legal for him?

Here's a revelation I'm finding out. The Drunken Bishops… they're super powerful. More than I thought. They ruin everything in the end game. It's like going up against the Sicilian when everything that can go wrong for you… starts going wrong for you!
Therefore, a truism may be:
Only exchange a Drunken Bishop for another Drunken Bishop.
They get out of corners without getting trapped whatsoever. In fact, they'll get out of your corner, and in the process leave your corner in ruins. They take pawns like taking candy from a baby. They come out of nowhere, post up on perfect squares, and you can't even attack them directly.
Combined with a piece to help them, like a Queen, where just a normal Bishop could be in the way, the Drunken Bishops don't have that problem at all as they capture two squares in front of them, and can keep that momentum going, and going, and going.
Damn they're scary!

Just so everyone knows, I'm liking Bf6, too. But, I'm not liking taking the Rook in the corner if the Knights, both Black and White, fall.
Let him play his Rook out of the corner. We play b6. (pawn up)
Hopefully he will have gone on a rampage for our pawns with his Queen, or waste a move getting his Rook out of the corner. He's about to get checkmated if he isn't careful. He may be forced to exchange Queens. Then we waylay his exposed King. He won't even know what hit him!

So let's analyze Bf6. If ed5, Bxa3, he has 3 options. Bd2, Qe2 and Qe3. On Bd2 we can go Bxd2 ~xd2, and ed5. We're up a pawn and the DSDBs have been traded off. After Qe2 we have ed5 and are up a pawn again.

All I know is if he doesn't bring that light squared Drunken Bishop out, pronto, he's in for a hurtin'.
JARP, just keep playing with the pieces, and us playing the b6 move ASAP.
Together, the Drunken Bishops can attack nearly everywhere. His Knight is in his way, his d4 pawn is in his way. By conventional wisdom, where his pieces would be routinely good for him, now they're just in the way.
If he moves his Rook to the light square, we can capture it and say Check.
All sorts of good things may be headed our way. But we do need to think them out.
Glad we have days to work the problem.
I think there may be a mate around eight moves out. That's how dire his situation is.
But a cursory inspection of the board doesn't reveal this at first, or even second, glance.

Current Position (Black to Move)
Interesting. (I think I'll stop trying to predict how Martin will move.)

Currently investigating one candidate move: b5!
If the Knights exchange and he takes the poison pawn, he loses the game.
(he won't take that poison pawn, though)
I'll be looking over the b5! move for the next 48 hours; every iteration/ramification I can imagine.
Give me time, please. (or at least… time enough to say I don't like it anymore)
The intent of the move is to open up his Kingside flank where he is most vulnerable, and continue to develop our Drunken Bishops to powerful squares.
Bob
We can also go for Nf4 Qd2 Bf6. I believe Qd2 is vad for him, as we now have Nxg2 as a possibility, and the Na3 would still be under fire.