Not much improvement when the extremely obvious move is the right move. But I suppose Rh8+ to allow queening with check is slightly less obvious, and instructive for rank beginners.

1. Re8 Rxd7 2. Ng6 Rd2+ 3. Kxe3 Nc4+ 4. Kf3 Nd5+ 5. fxe5 Rd3+ 6. Ke2 and there's nothing left for Black

1. Re8 a3 2. Rxd8 a2 3. Rh8+ Kxh8 4. d8Q+ Kh7 5. Ng6 a1Q 6. Qh8#
2. Re8 Nxd7 2. Rxd8 Nxe5 (Nb6 3. Ng6) 3. fxe5 wins