It's funny that you wrote 2...Ne4 and 2...Ne4, repeating the same move twice, because the computer analysis display for this problem shows the best move is 2...Qxh3 and the second best move is 2...Qxh3

Must be some kind of bug that repeated 2...Qxh3 instead of putting 2...Rxh3 for the second move.
Also, the top 4 moves are all over +3.0, so this problem should have been thrown out by the generator.
I'm sure Richard can explain all of this!