Okay, I think I might be on to something here. You know how Excitebike, Wrecking Crew, and Mach Rider have the Save/Load features in the editor? And how everyone assumed for years that they do nothing because it was originally for the FDS? I've noticed something that suggests this is not the case.

Try this:
Fire up any NES game with an editor and Save/Load options. Make some basic level design. Now, turn the volume on the TV up quite a bit and hit Save. Hear that? If you've ever played Supercharger or C64 tapes through an audio cassette player, you should recognize this instantly. It's actually saving the data via an encoded audio stream! You can hear a lead-in signal (probably around 2200 Hz or so) for a few seconds, followed by the actual encoded data.

So now the real question: how do we get the data back in to the NES? The Famicom had an actual microphone input from the controllers, so I have no doubts that there's some way to do this. I suspect that the audio input lives somewhere on the expansion connector underneath the NES. The problem is that I'm not familiar enough with the chips on the NES board to know which line I should be poking at. Has anybody ever figured out which pin on the connector corresponds to the audio input? If not, I'll just connect one wire to ground on the board, and try playing back a recorded stream into each pin sequentially, but I'd like to be a bit more scientific about it first.