12.Qf5 axb6 13.Nc7+ Kd8 14.Nxa8 Qxa8 15. Qxb6+ Ke8 16. Bc4 seems like only a small advantage for white since he is somewhat less in material, but has pressure on black.

12.Qf5 axb6 13.Nc7+ Kd8 14.Nxa8 cxb5 15. Qxg4 Qxa8 doesn't look too bad for black.

In short, I think your mainline seems to lead to the most advantage black can achieve.

12.Qf5 axb6 13.Nc7+ Kd8 14.Nxa8 Qxa2 as you pointed out earlier seems very good for black, almost definitely winning. Amazing that such a seemingly strong position can be refuted.

I made an error in my earliest analysis. When I suggested that 16...Qa5+ wins the white queen, I did not notice 17. b4 (nor the fact that the king could still move!) ;) After seeing your analysis, I know I have to take up correspondence to become a semi-decent player. I've been playing too much blitz and I bet there are a couple errors above. ;)