Well, it occurred to me that since the danmakufu scripts for this game are still user-readable, I'd try looking around for what the conditions to unlock extra REALLY are. Surprisingly, as best I can tell, it really does only require the completion of two scenarios (by the current shot type). I don't even think it matters whether you continued or not, or what difficulty it is. I wonder if it's not saving the clear data correctly? I know that sometimes the game bugs out and displays the wrong name for the boss I'm currently fighting, so perhaps it's possible.
However, after some more investigating, it occurred to me that the quickest way to actually unlock it, since it should already BE unlocked, as far as I can tell, was to simply alter the code for the extra-stage check to always return true. Simple enough.
I'm still tempted to try tracking down what the actual problem is, though. >.> But goodness only knows how long THAT might take.