Great thing about the internet: You can post a question at 4:15 in the morning, go to bed, get up and there — in your mailbox along with the ads for penis enlargement and guaranteed credit cards — is your answer.
Mike Zeidler informs me that "The Average Giraffe" was released by the Four Lads on Columbia Records #40490 but doesn't seem to be available on CD. And "Hit Record" was recorded in 1962 by Brook Benton (Mercury #71962) and is on this CD. Time-stamped about four minutes later was Ed Golick's message with the Brook Benton I.D. Thanks, Mike and Ed!