ConstantImprovement: So, let us have a look at the possible motifs:
1. First and foremost, Re7: as a sacrifice that takes away an important defending piece: The Black Bishop is potentially protecting f6, g7 and h6 against a White attack.
2. The lounge Nf5 (After Re7: or in itself) is bringing one piece closer to the King.
3. The sacrifice Ng7: (After Nf5), perhaps followed by moves like Kg7: Qf6+ Kg8 and either Bh6 or Rf3, eyeing g3 with mate after Rfe8 and Bh6.
4. The move Bh6 (After Nf5 or in itself) with the pawn cover intact, threatening Bg7: (Or Ng7:). There could follow (at the Nf5-lines) h6: Nh6+ Kg7 (Kh8) Qf6#.
5. A mate of Knight and Bishop after Nf5 and a move like Bg5. Without the g7-pawn there is a mate like Nh6+ Kh8 Bf6#.
Let us begin with some tries:
I. 29. Bg5 f6 30. Nf5 e5: 31. Ne7+ Qe7:
(Kh8 32. Qf8: Rf8: Rf8:#) 32. Be7: Rf3: 33. Rf3: Re8 34. d6 Nc6 and Black is a pawn up with the strong paased pawns.
II. 29. Nf5
1. 29. .. Bf6 30. Nh6+
a. 30. ... Kh8 31. Rf5 threatening Rf6: f6: Qf6:# (motif) 31. ... h6: 32. Rf6: with a strong attack
b. 30. ... h6: 31. Qf6: (threatening 32. Bh6 and 33. Rg5#) 31. ... Qd6 32. Bh6: Qf6: 33. Rf6: and 34. Rg5# follows.
2. 29. ... Bc5 30. Bh6 with a strong attack, see 30. ... h6:? 31. Nh6:+ and 32. Qf6#
3. 29. ... Bd6 seems to hold, 30. Nh6+ h6: 31. Qf6 Be5: 32. Qe5: Qd6 and Black is a Rook up.
III. 29. Bh6 with threats like Bg7: Kg7: Re7: Qe7: Nf5+ forking King and Queen or Qg3 g6 winning at least an exchange.
1. 29. ... h6: 30. Nf5
a. 30. ... Bf6 31. Nh6:+ and 32. Qf6:#
b. 30. ... Bg5 31. h4 and the attack continues, but probably not strong enough to break through
2. 29. ... Bf6 30. Qf6: f6: 31. Rf6: Qg4 32. h3 Qh4 33. R1f5 with the threat
of Nf3, but after 33. ... Qf6:! 34. Rf6: a5, Black is still winning.
IV. 29. Re7: Qe7:
1. 30. Nf5
a. 30. ... Qe8 (d7, c7, b7, a7, c5) and
now 31. Ng7: or even Bh6 should win right away (h6: Nh6:+ and Qf6#; else Bg7: next move, followed by Qg3 etc...)
b. 30. ... Qf6 31. Nh6+
b1. 31. ... Qh6: 32. Bh6: h6: 33. Qf6 with a winning attack because of the mate threat Rf3, Rg3#. 33. ... Rc8 34. h3 Rc7 (So that the f-Rook can move) 35. Rf3 Re8 36. Rg3 Kf8 and now Rg7, Rh7:, Rh8 should be enough, combined with a timely d6.
b2. 31. ... Kh8 32. Qf6: f6: 33. Bd4 should win, for instance 33. ... Kg7 34. Nf5+
b21. 34. ... Kh8 35. Bf6:+ Kg8 36. Nh6#
b22. 34. ... Kg8 35. Ne7+ Kg7 (Kh8 36. Bf6#) 36. Bf6:+ Kh6 37. Rf4 and 38. Rh4# follows.
So, let us review:
Not all of our motifs became visible during our analysis, but new, basic ones like the Nh6:+, Kg7, Qf6:# - sequence emerged. The final mate with Bishop and Knight working together to bring the King to the Rook was also noteworthy.
At the end, our main line:
29. Re7: Qe7: 30. Nf5 Qf6 31. Nh6+ Kh8 32. Qf6: f6: 33. Bd4 Kg7 34. Nf5+ Kg8 35. Ne7+ Kg7 36. Bf6:+ Kh6 37. Rf4 Kh5 38. Rh4#