So would you “clearly” describe how that passage works into the end times? Does Christ fight Armageddon at the same time we are being “caught up” or is that different?
I'm not sure. It seems to me though there is quite enough of a possibility that after He returns, but before raising the dead, He could "fight Armegeddon". That is, the passage in 1 Thess doesn't necessarily preclude something else He might do after He returns. However I think the timeline as far as the raising of the dead and the "rapture" of the believers is concerned is pretty clear. The dead are raised before all believers are taken to Heaven. Whatever may happen before, or even in between isn't necessarily prohibited by Scripture.
All that said, I'm not sure which event or events you're referring to when you say "[Jesus] fights Armeggedon". Just out of curiosity, as again, 1 Thess doesn't say the *only* thing Jesus will do when He returns is raise the dead and then bring all believers to Heaven.