Ugly, but yeah I think you got them all(This should cover everything, up to symmetry and mirroring.)
I don't see why.For there to be a second god's number, there has to be a 19 move strong or lower position that cannot be solved in 20 moves exactly.
We already know that GSN exists, so you're claiming there is a position that cannot be solved in exactly 20. Was that proven somewhere?
This makes no sense to me. How could a single position prove that?a position that proves there is a second god's number