What is the strongest continuation for Black?

ICC tourney 1312 (12 3), Internet Chess Club
Analysis of Blacknight101 (1596) vs. xiaoqixia (1617)

1 2 3 4 5 6 7 8 h g f e d c b a +5

(black to move) 1. e4 e5 2. Nf3 Nf6 3. Nxe5 d6 4. Nc4 Nxe4 5. d4 Be7 6. Nc3 Nf6 7. Be2 O-O 8. O-O Bf5 9. Bd3 Qd7 10. Ne3 Bxd3 11. Qxd3 d5 12. Qb5 c6 13. Qb3 Re8 14. Bd2 Bd6 15. Ne2 Ne4 16. Bb4 Bxb4 17. Qxb4 Na6 18. Qb3 Nd2 19. Qd3 Nxf1 20. Rxf1 Nc7 21. Nf4 Qd6 22. Nh3 Qg6 23. Qe2 Ne6 24. f4 Nxd4 25. Qf2 Nf5 26. Nd1 h6 27. Kh1 Re7 28. Rg1 Rae8 29. g4 Ne3 30. Nc3 Qxc2 31. Qh4 Qxb2 32. g5 Nf5 33. Qh5 Qxc3 34. gxh6 g6 35. Rg2 Re3 36. Qg4 Rxh3 37. Rf2 Re1+ 38. Kg2 Rxh6 39. Qg3 Nh4+ 40. Kh3 Nf3+ 41. Qh4 Nxh4+ 42. Kg4 f5+ 43. Kg5 Rh5#

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Pawn promotion:
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Click here for 34. Qg4.
Click here for 36. Ng1.