I think the thousand-year reign begins after Armageddon and after Satan is locked up in the abyss. With no one to lead mankind astray, the people and animals will all live in peace and harmony. That means the Millennium. At the end thereof, Satan is released, he stirs up the wicked, there's a brief battle of Gog and Magog, then all of Jehovah's enemies and Satan, himself, will be destroyed. The other thread related to whether Satan was alive or dead (meaning existent or nonexistent) during the thousand years.
Conventional Christian exegesis is divided between, generally, those who believe in literal prophecy and those who believe in replacement theology. JWs tend to go for the latter. Funny, they believe in literal prophecy up to a point, then, suddenly, it's all spiritualized. Nothing means what it says. And the Governing Body gets to determine what the prophecy means.