After reaching out to every researcher who cited the manuscript, John Kennison was kind enough to find and scan his copy of the untitled manuscript containing the crude and precise monadicity theorems. I have uploaded it to the nLab for posterity: Jon Beck's untitled manuscript. This copy was distributed at the Conference Held at the Seattle Research Center of the Battelle Memorial Institute in June – July 1968, though evidence from citationcitations suggests it was first distributed as early as 1966.