Dear Mr. Santos,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located Records Related to "The History of Pilotless Aircraft and Guided Missiles", 1953 - 1958 in the Records of the Bureau of Aeronautics (Record Group 72) which includes information on the Regulus missile. The Records of the Bureau of Ships (Record Group 19), the Records of the the Bureau of Ordnance (Record Group 74), and the Records of Naval Operating Forces (Record Group) also have series which may include information about the USS Randolph and the Regulus missile. These records are in the custody of the National Archives at College Park - Textual Reference (RDT2).
RDT2 will be pleased to make the finding aids to these records available to you or your representative in the Textual Research Room located 8601 Adelphi Road, College Park, MD, near the University of Maryland--College Park campus. The Textual Research Room (Room 2000) hours are 8:45 a.m. to 5:45 p.m., Monday through Friday, except legal holidays. The RDT2 consultation room hours are 8:45 a.m. to 4:00 p.m., Monday through Friday, except legal holidays. No appointment is necessary. Prior to your visit, please consult College Park websites at https://www.archives.gov/dc-metro/college-park/, https://www.archives.gov/dc-metro/self-service-copying.html, and https://www.archives.gov/research/start/getting-started.pdf.
Please be aware that records regarding the deployment of nuclear weapons may still be classified. It may be necessary to request some of the relevant records under a Freedom of Information Act request or a Mandatory Declassification Review.
We hope this information is helpful. Best of luck with your research!
An excellent secondary source on the Regulus missile is the book “Regulus: The Forgotten Weapon” by David K. Stumpf (Turner Publishing, 1996). Page 91 discusses the Regulus deployment aboard USS Randolph (CV-15) in 1956. As to the Regulus launch capabilities aboard the Randolph as compared to that aboard the USS Hancock (CV-19), Turner noted that GMGGRU-2 made use of an improved Induced Pitch Launcher (IPL) to allow the carrier to launch Regulus from its H-8 catapults. The IPL allowed the Regulus to use a higher angle-of-attack at take off, which, combined with the powerful thrust of the missile’s Jet Assisted Take Off (JATO) rockets, allowed the Regulus to leave Randolph’s flight deck in the fashion shown in your second image.
I hope you find this information useful.
That pretty much answers my question. I will also take Jason's advise and pull up those files in Archives 2.