This is something I've wondered about for years, and am surprised I've never seen any mention of it. Back around January or February of '96 there was a little blurb about Tiny Music, right before it came out. Two of the track titles that were mentioned were "Tumble in the Rough" & "Barbarella". By the time the album came out, I figured this mysterious "Barbarella" track had its name changed to "Daisy" or "Lady Picture Show" or any one of the other songs. Two years later, the SW version of "Barbarella" comes out on 12BB.
Given that I'd heard this info within 1-2 months of Tiny Music's release, in hindsight it seems like this never-before-heard STP version of the song was removed from the album at the last minute? No idea why.