Is there a reliable source on the army numbers in these
wars?
I seriously doubt that. The only specific number I can recall is
Turgon showing up unexpected at the
Nirnaeth Arnoediad with an army of ten thousand. JRRT was vague on all sorts of numbers, including populations. But as to
wars and battles, I can well imagine that he had little interest beyond general description and (very) few details. He had
been in war, in one of the most massive, and costly,
battles of the First World War, the Battle of the Somme starting on 01 July 1916, losing two of his three closest friends in that battle, one on the very first day.
I can well imagine JRRT being horrified at the morbid interest taken by many who have
not experienced war (and should be thankful for that) in all sorts of "war games". The concept of war "
games" might very well have made him feel sickened.