Owen Bradley, who produced many of Monroe's Decca sessions, played organ on three of them: March 17, 1951 (Swing Low, Sweet Chariot/Angels Rock Me to Sleep), March 19, 1958 (Life's Railway to Heaven), and March 31, 1958 (Wayfaring Stranger/House of Gold) My source is Neil Rosenberg's Bill Monroe and His Blue Grass Boys: An Illustrated Discography, published in 1974 by the Country Music Foundation. Rosenberg's book states that Bradley didn't play organ on Precious Memories, also recorded March 19, 1958, but if there's organ on that track, Rosenberg's wrong; it was Bradley.
Researching all the bluegrass historical material I can dig up, I can't find a mention of what type of organ Bradley used on the Monroe sessions. A narrative of Bradley's production of Patsy Cline's Crazy in 1961, however, mentions him "directing the sessions from behind a small Hammond organ," and this is as close as I can get to a definite ID. I would think that some organized research on Bradley and his Quonset Hut Studio in Nashville, might yield more info on the gear that was used there.
Gibsn: '54 F5 3pt F2 A-N Custm K1 m'cello
Natl Triolian Dobro mando
Victoria b-back Merrill alumnm b-back
Stradolin Vega banjolin
Sobell'dola Washburn b-back'dola
Eastmn: 615'dola 805 m'cello
Flatiron 3K OM