Epstein did not give Storm a real shot at the big time because he "didn't want any major competition" for The Beatles, Caldwell believes.
The tapes include tracks recorded at the Jive Hive club in Crosby, north of Liverpool, and at Storm's house, known as Stormsville, where bands including The Beatles would get together once clubs like The Cavern had shut at night.
"I suppose these tapes have been in an old sealed box ever since [they were recorded]," Caldwell said.
Author and Radio Merseyside presenter Spencer Leigh said the group were "crucial to the early years of Merseybeat".
"Even though the playing is very rough and ready, they have tremendous presence and were probably considerably better than the Beatles were in March 1960," he said.
Iris Caldwell's son Adam F, a Mobo Award-winning drum and bass DJ, said the recordings allowed a new generation to hear his uncle's style and personality for the first time.
"The quality of the tape left a bit to be desired - it was over half a century ago - but the spirit and rawness suggest a whole scene waiting to happen," he said.
"I am so proud that my uncle was, as has been suggested to me often, the father of the Liverpool sound."
Storm's on-stage antics included climbing up to the high diving board during one gig at New Brighton swimming pool.
"He had a cloak on and stripped right off to his little gold Speedos," Caldwell recalled. "He dived into the water, came up and carried on singing the song.
"Another time, they had a box on the side of the stage. He made his entrance by jumping from the box onto the stage. He did manage to break a couple of ribs but he still finished the spot and then went off to hospital."
Other than Starr and guitarist Lu Walters, whose whereabouts are unknown, the original members of Rory Storm and the Hurricanes have all passed away.