Testrun of Fantasy Zone in 3:46 using demo manipulation
So, it turns out that by "surviving" long enough during a demo until Opa-Opa destroys the last base, you can get control of him, but sometimes he just comes to a dead stop and you can't move around, for reasons I don't know.
So my approach was as follows: get to the demo of round 7 (the last regular level) as fast as possible. You don't have to sit through the demo in its entirety, you can reset once the demo starts and the game will play the next demo after the title screen. But I had to play round 1 a bit, to get $ 3000 to buy upgrades, since I wasn't able to defeat the boss' final snake with default speed/weaponry (but it might be possible). Here's hoping that someone knows what's really happening during the demos, so that it can be manipulated more effectively. The bossrush is most likely also improvable with different money<->weapon management.