Here is some more information. It must be a legal game. All moves must be legal, and if a king were ever in check it must get out of check. Kings may not be captured. :-)
On the existence of a potential solution, I'll just say for now that if it were a homework assignment and I wrote all that I know on the topic, I would very likely get an A. I don't want to give too much away, since a bit of the fun here is to try to out-do a previous solution. That, in conjunction with various lower bound style statements on minimum move amounts will give you an idea of "how close" you are theoretically. I consider the problem solved if you can prove a lower bound using a set of statements and then give an example solution using exactly that number of ply.
lol,