According to the question, Earl Mack's real name would have been Earl Gene McRaney. Born '31, died just a few years ago in '03. Have seen no evidence of any other singles or any other work with/from that record label.
The Alabama Music Hall of Fame did not seem to have anything. I've sent a brief query to the public library to see what they have. He was born more Southernly so it is possibly that someone around the Montgomery area has something, but I figured I'd toss this out there just in case someone was a local rockabilly scholar.
UPDATE. I have the following additional information, which might be of some interest.
The address in the last 50's, early 60s:
P.O. Box 1268
There were at least two styles of label. The Earl Mack track in question used the original: http://www.youtube.com/watch?v=q5aEDSlKdbw,
...later acts used a modified one (see: The Viscounts: http://www.youtube.com/watch?v=--bFprDcLwE).
Looks like the producer was By-Nash of Nashville, which was still around into the early 80s at least and might still be around, just in Florida now.