Thanks for the tip; I’ll check it out. The first thing that popped into my mind when I first heard it was
Alice, so I would not be surprised if it was afterall.
I have been thinking about that game a lot recently, so I may yank my discs and give the game another play soon.
*UPDATE*
I just downloaded the songs and you are right, it is the
Alice soundtrack!!! Thank you! My favorite track was the one labeled 07 which in that page is listed as “09-i-m-not-edible”; it is delightfully demented.

The question now is why the ones that I have are different from the ones on that page. They are the same songs, but different versions. I suspect that one of them is from the game itself (in-game music), while the other is probably from a stand-alone CD soundtrack release.
I am definitely going to have to get my Alice discs to check (and play again) now…