Eugenics Wars thing is actually pretty hilarious, and timing for it has been contradictory at least since the Wrath of Khan, and made even worse by introduction of World War III by TNG. Like I recently noted on another forum, all of this is canon:
1) Eugenics Wars were the
last human world war.
2) Eugenics Wars happened in the 1990's.
3) Eugenics Wars happened two centuries ago from 2260s.
4) World War III took place in the mid 21st century.
All of these literally cannot be true at the same time!