But I still have no clue for the correct answer, even after going trough the list of winners in the above link.
That's the award, right enough! To summarise the three most important clues so far:
The novel won the John W. Campbell Memorial Award.
The author's dead, and would not be thought of by most as a writer of science fiction.
The novel is set in an alternative timeline to our own.
The Alteration by Kingsley Amis (1922-1995) - John W. Campbell Memorial Award in 1977.
Alternate parallel-world novels in The Alteration
Just as The Man in the High Castle features a book entitled The Grasshopper Lies Heavy, depicting a world (but not our own) in which the Allies won World War II, so The Alteration refers to an alternate history book by one Philip K. Dick entitled The Man in the High Castle. This book-within-a-book depicts a world in which Stephen II was never born, so the "Holy Victory" never happened, and Henry VIII became king legitimately. As in our world, Henry married Catherine of Aragon, but their son Henry, Duke of Cornwall survived infancy, becoming Henry IX in 1547. Martin Luther became "schismatic" in this world, as he did in our own, and a "Union" of former English North American colonies breaks away in 1848 instead of 1776.
Galliard, an alternate-universe counterpart to Keith Roberts's Pavane, is also mentioned in this tribute to the subgenre. (The Galliard and the Pavane were both forms of Renaissance dance.)
When we wuz young, these trivia questions were actually pretty dang trivial, we didn't need no newfangled gizmo's like Google-fu! We had it all in our own heads, young man!"
New question: we are looking for a military spaceship, destroyer class, built by humans on or from Earth. It later became the flagship of a fleet attacking Earth.
First thing that came to my mind: EAS Agamemnon - Omega class Destroyer acting as Sheridan's flagship in Earth Alliance civil war 2261 in Babylon 5 (season 4)?
First thing that came to my mind: EAS Agamemnon - Omega class Destroyer acting as Sheridan's flagship in Earth Alliance civil war 2261 in Babylon 5 (season 4)?