On June 5, 1965 a C-119 was disabled on
Grand Turk island. That evening, a second C-119 was dispatched from Homestead AFB with a crew of 5 and an additional 5 mechanics to repair the stranded plane. It was this second plane which vanished. On July 18, 1965 debris of the C-119 was located on Acklin Island.

It was quite easy to find an account of the missing
C-119 which disappeared in early June 1965. Note that it differed in several ways from your discussion.