My favorite truly obscure band would be Ayane (formerly known as 彩音 before the vocalist went solo)
While 彩音 released a couple singles and a minialbum, they weren't exactly impossible to find. On the other hand, Ayane had two singles limited to 20 copies each as well as a full album that probably only exists in the single digits at best. I nearly wouldn't believe that the album even existed at all if I didn't see a single trader with it on their list (though they absolutely refused to trade it for anything, so it very well could have been a fake listing).