@K-Huang
1. If there is an impractical puzzle, should impractical choices be made. If you're in a terrible position, should you make terrible moves? Why then should illegal moves be necessary? This is simply a puzzle I created.
2. I do not know what the solution is. However, I am quite sure that with best play, white should be able to win.
Well, I think the visual display that results when you very quickly work through ipburke86's solution is quite impressive! It reminds me of a scene in Alice in Wonderland. Perhaps we should just consider this solution as a work of art, and consider the puzzle solved (and it may actually be).
@k-huang: While the position is illegal, one could work on it with legal moves, and I imagine that the idea was just to have fun!