I love stories like yours. I have one as well. A friend of mine (back in the 90s) told a story of how he was washed overboard of a SSN returning to port in Japan. While they attempted to find him, it was stormy and rough. He floated just 24 hours, but he said the night was pretty rough. He did find God however, made his peace and after that he said it was the most beautiful and moving experience thus far.
Yours reminded me of another. As an NROTC middie I was on an LPD going from Okinawa to Korea, circa 1978. We had a bunch of Marines on board, hauling them to Pusan. At sunset in the Sea of Japan, calm water, two separate guys, a Marine and a sailor, both reported seeing a man overboard, waving his arms for help. Because two different people reported exactly the same thing, but a little delayed, the report was taken 100% seriously. We did an expanding box search pattern all night, using our old Starlight scopes etc. The Japanese reported that yes, they had lost a fisherman off a boat. We all KNEW the man was out there, alive enough to wave his arms frantically at a passing ship.
But we never found him. What a night he must have had, watching us boxing grids all around him with no luck.
:^(