I already wondered if 1. e8=N wouldn't work with 2. Nc2. So here it goes:
1. e8=N Bd6
2. Nc2 no escape from N(x)b4(+)/N(x)c7(+)
1. e8=N Rc6
2. Nc2 no escape from N(x)b4(+)/N(x)c7(+)/cx(bQ)b6 except for...
2. ... Bxc5
3. dxc5 and now really no escape left to abovementioned threats.
Think twice before speaking once. 2. Nc7 might be a checkmate as well. Good problem then [edit2] Speak a lot before thinking - after Nc7+, c6 becomes vacant, so perhaps this might be the solution?!