I can't believe my luck. Today I found
another Nyko PlayCube, and it's
completely different in design.
This second one
does appear to work perfectly with the GameBoy Player!Here, I'll go into detail.
This is the first PlayCube I found.I doesn't seem to work with the GBP at all (although I haven't gotten my hands on my brother's early-model Dual Shock yet, but I don't think that'll matter anymore).
When you turn on the GameCube with the GBP and a Dual Shock attached through this one, the "analog" light turns on instantly, but when you get to the "GameBoy Player" screen (right before your GBA game boots up), the light shuts off. You can turn it back on if you like, but it won't do you any good. Nothing at all works.
The light doesn't shut off if you're playing an average GameCube game, and it works on them just fine, in case anyone was wondering.
This is the second PlayCube I found.When you turn the GameCube on with a Dual Shock and this PlayCube, the light on your Dual Shock will be off. And it won't turn on automatically. And none of the buttons work (analog or digital).
When you do turn on the analog, the sticks are completely miscalibrated. All of the digital functions work, but the analog stuff messes with your controls. This seems to be a problem localized in the PlayCube, because when I unplug the Dual Shock from the PlayCube "in-game", Samus keeps running around in circles. She stops abruptly if you unplug a normal GCN controller while you're playing. So it's gotta be the PlayCube itself that's still sending signals.
You can fix this by simply recalibrating the analogs. Press down X, Y, and Start (or rather, Triangle, Circle, and Start, since you should be using a Dual Shock), and hold them down for at least three seconds.
Once you do that, this PlayCube works perfectly. On a GameCube game,
or the GameBoy Player.

By the way, it seems that sometimes when you turn on the GameCube with the "PlayCube #2", the Dual Shock's light will turn on instantly, and it will remember your analog recalibration. This doesn't seem to be a problem, and the light won't turn off when you hit the GameBoy Player screen. I'm not enough of a techie to know why that is or what it means, or why the "PlayCube #1" doesn't work, but it might be of some use to someone.
Or at least, that's how it's working for me. Any feedback from anyone else about what type of PlayCube they have, or if anyone has gotten anything else like the "Cube JoyBox" to work would probably be a good idea.