We could simply stop accepting recordings and start insisting on sheet music, but the only thing that really does is close out submissions of improvised music -- it doesn't increase the amount of "source" available.
One thing you could try is using a pitch detection algorithm to come up with a notated approximation. If Auto-Tune can recognize what notes T-Pain is trying to sing, and if your phone's GSM speech encoder can compress your voice into fewer bits, a similar pitch detector can recognize what notes your musician improvised, provided the instrument was miked in a way that reasonably isolates a solo performance from other band members' instruments. So you could stop accepting fully mixed improvised recordings and insist on multitrack masters and reward someone else for notating it.
Give the midi file to a random person with a computer and it's going to sound like it's being played on a gameboy.
Which Game Boy? The Game Boy Advance is capable of playing an orchestral recording. I even wrote a music player app for it back when I was in the GBA homebrew scene. There's a huge difference in capability between a Game Boy Color, which compares to a Nintendo Entertainment System, and a Game Boy Advance, which compares to a PC with an old 8-bit stereo Sound Blaster.