Ah, I've found the answer to my own question.
The slightly paradoxical 15...Qb6! when:
A) 16 a3 Qe3+ 17 Kb1 a5! (17...Bxc3 18 Qxc3 Qxc3 19 bxc3 is possible as well) 18 Qe4 (18 Qb3 Qxf4=) 18...Qc5 and Black has a serious initiative.
B) 16 Qxb6 axb6 and now:
  B1) 17 Ne4 Rxa2 18 Nxf6+ gxf6 19 Bc4 Ra5 - despite Black's mess of a structure, I don't see a clear way forward for White.
  B2) 17 Bb5 Bxb5 18 Nxb5 gives back the pawn in exchange for breaking the blockade on the d7 square. However, after 18...Rxa2 19 c3 Ra5 followed by ...Rd8 and ...Rd7, I don't see any problems for Black.
  B3) 17 Bc4 Bc6! (I think this is more accurate than 17...Bxc3 18 bxc3 Bc6 because now 19 Rhe1!; White can ignore the threat to his g2 pawn, because without the Bishop on f6, the d-pawn is far more dangerous.) 18 f5!? (18 Rhg1 Bxc3 19 bxc3 Ra4=), and now a sample variation could go 18...Bxc3 19 bxc3 exf5 20 Rhe1 b5 21 Bd5 Rfd8 22 Kb2 Kf8 23 Re7 Bxd5 24 Rxd5 Rxd6! 25 Rxf7+ Kxf7 26 Rxd6 f4 with an ending that should be okay for Black.
This can also be played if White tries 15 Qe3 instead of 15 Qb4, as after 15 Qe3 Qb6!, I don't really think White has anything better than taking on b6.