'Unknown' is relative of course, but here are some other recommended shows which have some kind of cast recording(s) or demo tracks available but which, to my knowledge, haven't had a major label cast recording release as such. (Some do have commercial cast recordings.)
Ghost Quartet - spooky, melancholy interweaving of various story threads and ideas. (If you're a Dave Malloy fan, there are selected songs available for listening from his other 'unknown' shows on his website as well.)
A Very Potter Musical series - good silly fun, though you may need to be a Harry Potter fan. The same team's Disney/Aladdin/Wicked parody 'Twisted' is also fun.
Futurity - not sure if I can summarise or even fully know what this show is about, but I enjoyed the album! This show is even having its libretto published as well, straining its 'obscure' credentials.
Shaina Taub's Shakespeare musicals - she has released self-sung demo cast recordings of 'Twelfth Night' and 'As You Like It'. I haven't listened all the way through, but what I have heard sounds good.
Picnic at Hanging Rock - there are a few haunting demo song recordings around. IMO this show has a bit of a 'Goblin Market' vibe, if that means anything.
Peter Pan (Stiles and Drewe) - it's not top-tier but is, in my opinion, closer to the spirit of the original play and novel than other musical versions I've heard.
Cannibal! The Musical - soundtrack for Trey Parker and Matt Stone's early movie musical effort.
James and the Giant Peach - Pasek and Paul kid-friendly show.
21 Chump Street - not that obscure these days, but the cast recording is on iTunes and Spotify.
If you search this board for threads on 'obscure' musicals, you'll find some other recommendations.
By the way, according to https://unsungmusicals.org/umc-digital/ a company called 'Unsung Musicals' will be releasing a couple of abridged recordings in November of some older relatively unknown musicals, 'Gatsby' and 'Peggy-Ann'.