Exciting 7th game

The 6th grader had a nice assault against his opponent's King but had lost a knight and a rook in the process. She began an assault of her own and he switched to defense when he needn't. I don't think he can win if she plays perfectly, but I think he had a chance if he just said to himself "I'm down two pieces and if we make it to an end game, I'm going to lose. So what have I got to fear - I might as well keep up my attack and see if I can checkmate her."
What move could he make to keep up the the attack against her king?

If you said Nxg3 or Bxg3, you are an attacker!
Let's try it Nxg3 20. hxg3 Bxg3  (Now she has to be careful! Kg2 or Ng2 and it's mate!) 21.Qg2 Be5 22. Rd1 g3 23. Qh1 (avoid the skewer and desperately trying to trade queens - not many other choices) Qg5 24. Ng3 (White has to stop the pawn and guard e3 lest he play d4 which would lead to checkmate exd4 Qe3+ Rf2 Qxf2#) Bg4
25. Qxh7? Rh8 26. Qf7 Rh1+ 27. Kxh1 Qh6+ 28. Kg1 Qg2# and he wins!
How about 25. Rb1 Rd6 26. Qh4 (the only move that saves the game) Qg7 27. Nf4! (This was a hard to find defense - it interferes with with bishop's protection of g3! If she doesn't find this, Rh6 wins for our player.) g2 with still some interesting possibilities.

Now let's try Bxg3 20. hxg3 Nxg3 21. Qg2 Nxf1 22. Qxf1 Rg8 23. Qf4 (with double threat Qb8 and Qxh6) This didn't work as well. Two bishops are better than a bishop and a knight. We had control of two important diagonals in the first example.