It strikes me that this isn't a terribly interesting problem, since the "obvious" move (to pull out of atari) works, and since the contraint "black to save all stones" means that no other move can be considered.
Perhaps it would be better to ask the question: black to get the best endgame result (in which case pulling out of atari is wrong); or white to play after black pulls out of atari?
It isn't terribly hard to recompose the problem so that saving all stones is the best solution.
Therefore, I suggest the following:
Of course, I would appreciate if someone can check on the modified composition. =)