I ran across a website that listed the Dr. Demento shows in which Phil Harris recording of Elmer and the Bear were played.   Here they are if anyone has access to recording of those shows.

        06-17-79, #79-24                01-24-99, #99-04
        10-04-81, #81-40                11-14-99, #99-46
        12-26-82, #82-52                11-05-00, #00-45
        12-09-84, #84-50                11-04-01, #01-44
        10-23-88, #88-43                11-03-02, #02-44
        05-05-91, #91-18                11-07-04, #04-45
        11-07-93, #93-45                11-06-05, #05-45
        01-19-97, #97-03                11-05-06, #06-45
        06-15-97, #97-24