Marcel LaFollette's recent (2008) book, Science on the Air, provides a good overview of the history of the Radio Nature League. (You can read large portions of it via Google Books.) She draws heavily from correspondence between Burgess and Austin Clark of the Smithsonian. I don't know many radio scripts she had access to; I imagine there were a few copies included in the Burgess-Clark correspondence. I am indebted to her account for any behind-the-scenes context I provide. You can hear a conversation with her about the book on Mark Lynch's Inquiry program on WICN.
The radio scripts in the Thornton Burgess collection at the Howard Gotlieb Archival Research Center at Boston University can be divided into five periods. (Note: the dates ranges below indicate the scripts available in the collection. These may or may not correspondent to the date ranges of the actual programs).
1. Bedtime Story Radio Talks (WBZ November 26,1924 to December 17,1924) These were weekly ten minute talks on a variety of natural history topics. The "Sleep Fairy" bedtime story directly followed. (Note: Burgess began to appear on WBZ earlier in 1924; the numbered scripts in the HGARC begin November 26, with episode #2. Presumably, the talks began on November 19.)
2. Radio Nature League (WBZ/WBZA January 7, 1925 to August 2, 1930 with periodic breaks). These were weekly ten-minute to thirty-minute programs that featured Burgess recounting experiences and answering questions from RNL members. Some of the programs included guest speakers. This is the largest part of the collection.
3. Burgess Radio Talks (WBZ/WBZA-NBC November 27, 1933-December 29, 1934). These were weekly fifteen minute talks that also featured Burgess recounting experiences and answering questions from correspondents. The "League" framework was absent, however, and Burgess used the forum to promote his books and personal causes (e.g., anti-steel trap regulations). (Note: The HGARC lacks a script for the first show (November 20, 1933) and any scripts from January and early February 1935. It is during this period presumably that the new Brewer-sponsored format was established).
4. Radio Nature League on the Sun Glow Program (WBZ/WBZA-NBC and other New England stations, February 13, 1935-January 7, 1936. These were highly-produced weekly and twice-weekly half-hour programs that featured dramatizations of Burgess's and RNL members' experiences, as well as a rotating cast of visiting characters. The "League" framework was formally re-introduced but only a small amount of time was devoted to member experiences and questions. The program was sponsored by Brewer & Co., a Worcester, MA pharmaceutical firm. "Sun Glow" was a brand of cod liver oil. (Note: February 6--not in the collection--is presumably the date when Burgess announced the return of the Radio Nature League. January 7, 1936 is the last script in the collection from this period. It is unclear whether the program remained on the air after this date.)
5. Good Neighbors Club (WSPR February 7, 1939-July 4, 1939). Burgess briefly returned to the air on a program sponsored by the Women's Auxiliary of the Springfield branch of the SPCA. The format featured correspondents' experiences and questions and included some promotion of the SPCA's causes.
Next: Bedtime Story Radio Talks (1924)