While poking around on wikipedia I came across this;

"In 1963, a Hercules achieved and still holds the record for the largest and heaviest aircraft to land on an aircraft carrier.^[32] During October and November that year, a USMC KC-130F (BuNo 149798), loaned to the U.S. Naval Air Test Center, made 29 touch-and-go landings, 21 unarrested full-stop landings and 21 unassisted take-offs on Forrestal at a number of different weights.^[33][34] The pilot, Lieutenant (later Rear Admiral) James H. Flatley III, USN, was awarded the Distinguished Flying Cross for his role in this test series. The tests were highly successful, but the idea was considered too risky for routine carrier onboard delivery (COD) operations. Instead, the Grumman C-2 Greyhound was developed as a dedicated COD aircraft. The Hercules used in the test, most recently in service with Marine Aerial Refueler Squadron 352 (VMGR-352) until 2005, is now part of the collection of the National Museum of Naval Aviation at NAS Pensacola, Florida."

I wonder if they ever considered the C-123, which looked like a smaller, 2-engine version of the C-130?

There's a pic under 'operational history - military' at  Lockheed C-130 Hercules

Lockheed C-130 Hercules The C-130 entered service with the U.S. in the 1950s, followed by Australia and several other nations. During it...