I would imagine beevee means a regular curved soprano rather than any of the more exotic variations. The standard curved soprano also has the crook offset at an angle to the main body tube, and I find it very comfortable to play.
Talking of jams, I am often the only alto player among as many as six horns, all of the others being tenors (although one of them doubles on straight soprano). As noted by Tengu above when talking about the contrast between tenors and sopranos, even my alto comes across as a very different sound after all the tenors. Olivier's soprano doesn't quite come over in the same way, as his soprano style tends to be a little timid and polite (his soprano would probably work better without drums, or maybe with guitar instead of piano), but also as Tengu notes, even forty years after his death, Coltrane's sound and playing is still incredibly influential.
Cheers, Bob