Looking at the possible mating moves for Black, we quickly see that it has to end with Nxe2 mate. There is no conceivable way for White to force Black to play Rd6 in any final position, even if we could block the escape squares for White's king. So working backwards from the desired goal, we will end with 42. Qxe2+ (or possibly Rxe2+) forcing Nxe2 mate. Now all we have to do is fill in the remaining moves.
Clearly White is going to have to promote several pawns in order to block the squares on c4, c5, d5, e5, e4, e3. That's six promotions, and a seventh will be needed for the piece that makes the final capture on e2. We must make sure that Black is indeed forced to play Nxe2 at the end, which means (assuming we play Qxe2) that c1 and b1 have to be protected. A bishop on e3 can cope with c1, but White will need an eighth promoted piece to guard b1. So we must promote all out-pawns, (which involves capturing all Black's men except the knight), then get them to their posts for the final act. With 32 moves needed for promotions and captures, there is no scope for time-wasting.
The full solution begins: 1. e8=N, 2. Nxf6, 3. Nd5 then f6, f7 and 6. f8=Q, 7. Qxf3 and 8. Qg2] That is the most difficult move to find: the queen finds the only square to enable 42. Qxe2 without interfering with the moves in between. Now everything goes like clockwork: 9. f4, then f5, f6, f7 and 13. f8=B, 14. Bxh6 and 15. Be3, clearing the way for h6, h7, h8=R, 19. Rxh4 and 20. Re4.
The other h-pawn promotes to a queen at move 25, followed by 26. Qxb8 and 27. Qe5. Then 28. b8=B 29. Bxa7 and 30. Bc5. Two more promotions to go: 31. a7, 32. a8=R, 33. Rxa4 and 34. Rb4] completes the task of covering b1, then finally a4, a5, a6, a7, and 39. a8=N, sets up 40. Nb6, 41. Nc4 and 42. Qxe2+. A magnificent achievement, with two complete sets of white promotions.
With two rounds left to play in the Cafe Baroque tournament, scores are: McDonald 51 2 ; Whiteley 4; Britton and Dive 3.