I think one of the problems...I did specify just one...is a confusion of Wileys in 1944: (i) Capt. and Mrs. Herbert Victor Wiley--as you've pointed out, this Wiley was neither a vice admiral nor retired in 1944, when USS WILEY (DD 597) was launched, as christened by Mrs. Wiley. (ii) The ship's eponym, William Wiley, apparently a bold American seaman who was notable from the Barbary wars. (iii) The recently late (May 1943) Admiral Henry Aristo Wiley, captain of WYOMING (BB 32) in WWI, chairman of the U.S. Maritime Commission between the wars, and recalled from retirement to head the wartime Navy Board of Production Awards. I'm not absolutely certain, mind you, but I think the latter Wiley rose to the rank of vice admiral--thus the confusion--and was promoted to admiral upon retirement or death.
To repeat the history of rigid-airship adherent Herbert V. Wiley, he was promoted to captain on July 1, 1941, and after serving as ComDesRon 29, he commanded WEST VIRGINIA (BB 48) at the battle of Surigao Strait in 1944, winning a Navy Cross. Postwar, he remained a captain, and retired for reasons of health in January 1947, being promoted to rear admiral on the retired list on the basis of his award for valor in combat. Thereafter, as you have pointed out, he went into academia.
I have read several references to Vice Admiral Herbert V. Wiley, almost certainly an error, and very likely all such stem from the original error that Mrs. Wiley was the wife of Vice Admiral Herbert V. Wiley (Ret.), which we now know has two errors of fact. While I don't know the source of the original error, the fact that DANFS picked it up and ran with it doesn't help matters. My best guess, again, is that Mrs. Wiley was confused with the wife of Vice Admiral Henry A. Wiley....but now I wonder which officer's wife actually swung the bottle at the bow of USS WILEY, and if so Mrs. Herbert Wiley, then if she was the wife actually intended!
If Mark's information that Wiley graduated with the USNA's Class of 1915 is correct, what chance would there be of his rising to full lieutenant in a mere five years, even with the war intervening? And we still need to explain his Pay Entry Base Date of May 1911, which in most other instances is also the date of commissioning. But whatever, I'm sure that Herbert Wiley "used up" his one grade elevation in rank--to rear admiral--based on his Navy Cross. If he was buried as a vice admiral, it had to be for some other reason.