Part of the answer turned out to be that their website was Flash, so it was never meaningfully indexed, and their MySpace was never mirrored. A band can be entirely findable in 2006 and entirely gone by 2026 depending on which technologies they happened to pick.
It was eventually solved by searching on the producer's credits rather than the band's name, and then by two people replying to cold emails. Both the producer and the singer were generous enough to be interviewed, so there's some fresh detail in there about the recording session as well.
Sadly the ability to search via the usual suspects has diminished greatly from 2015 onwards, not all of it is on lack lustre efforts of search engines involved, some of the data had become just too hard to get from within forums where human intelligence rules. Of course the lack of competition from new search engines isn't good either, too many sites aim to block all but the top handful of bots from their content ...