Suggest one obsure album we all should hear

Obscure, you say?
Here's a good intro to Harry Partch, a brilliant iconoclastic composer who designed and built his own instruments and employs a microtonic (43-tone) scale:

Music of Harry Partch, Vol. 3: Sonata Dementia 
or
The Harry Partch Collection, Vols. 1-5
by Gate 5 Ensemble

Bring on the Night, Sting

Some excellent bands (from a 2016 post):
https://forum.audiogon.com/discussions/obscure-bands/post?postid=1346137#1346137

Particulars (since you removed the one album rule):
Bardo Pond / Dilate
Swans / Glowing Man
Tanakh / Ardent Fevers 
Lambchop / How I quit smoking
moe. / Wormwood
Alex Chilton / High Priest 
Blitzen Trapper / Fur
Mark Lanegan / Has God seen my shadow
Nico & the Faction / Fata Morgana
Brian Eno / My squelchy life
Spiritualized / Ladies & gentlemen we are floating in space
Tortoise / TNT
Thurston Moore / Demolished thoughts
Acid Mothers Temple / In search of the lost divine arc
Stone Jack Jones / Love & torture
Low / Drums & guns
Eels / Electro-shock therapy
Larkin Grimm / Parplar
Magnetic Fields / 69
MV & EE / Space homestead
Jenny Lewis / Acid tongue
Forest for the trees
Calexico / Spoke
Mono / Under the pipal tree
Mazzy Star / She hangs brightly 
Devendra Banhart / Mala
Castanets / Cathedral
Sparklehorse / It's a wonderful life
APSE / Climb up
Elizabeth Viagic / Stand with the stillness of the day
Industrial Tepee / What divine engine
Pere Ubu / Pennsylvania 
Beth Orton / Trailer park
Orso / Long time by
Tunng / Good arrows
Grails / Black tar prophesies 

There are many more (obscure music is my forte)... But that should keep you busy for a while :-)

The Mysterious Flying Orchestra 

A 1977 album from Bob Thiele

https://somehowjazz.com/mysterious-flying-orchestra/