Dinner with Chicago's finest

My friend Tim the detective bought me dinner on Taylor Street last Wednesday.  He's a very good chess player, so I showed him the Troitsky study.  In the process, we discovered that the 2...e6 sideline is trickier than I'd realized.

 

 

 Tim then showed me a position from a Facebook game (Chess with Friends) he was playing against a buddy from California.

Black to playTim played the natural 1...g2!  (In fact, he played it at the beginning of our dinner.) He showed me his analysis of 2.Bxh2: both sides queen, but Black is winning.  I suggested 2.Rxh2: that didn't work, either.  The variations were very interesting and went well with dinner.  Tim's buddy didn't find anything better, either. By the time we had finished dinner and moved on to skittles, Tim had an easilly winning position.

I went home and put the position on the computer.  Houdini found a draw for White: hmm, there's a reason the chess software engine is named after the escape artist.  (I had seen the basic idea, but over dinner, I'd been trying it one move too late.)

Match wits with the detective; can you find the drawing continuation that Tim and I missed?