Here's an alternate theory, instead of assuming there's a time paradox:
Timeline 1, 1981: At the end of Evil Dead 1, Ash burns the book and in a last ditch effort to save itself, the "Evil" rushes at Ash as it's dying and hurls him back in time. He defeats it again and time progresses to...
Timeline 2, 1987: This time, Ash is already established as the hero who defeats the book because of Ash being hurled back in time in Evil Dead 1. The events of Evil Dead 2 take place, with Ash, the chosen one, ending up repeating the most crucial events in the first timeline, albeit differently. This time Ash is the one attempting to send the book back in time, but he sends himself along with it. Eventually, Ash finds his way back to modern times and lives as a recluse until the events of Ash vs. Evil Dead.
Timeline 3: The Army of Darkness timeline branches off of Timeline 2, meaning MOST of Evil Dead 2 happened (with a different Linda), but there is less emphasis on other people from Evil Dead 2 (Annie Knowby not mentioned at all). Ash eventually gets sucked into the portal and comes out at a different medieval castle than the one at the end of Evil Dead 2, the castle of Lord Arthur. The events of Army of Darkness take place and Ash eventually returns to his own time. This Timeline lends its canon to the Dynamite comics. Indeed, characters like Annie Knowby generally aren't referenced in any meaningful way in other comics and games bearing the "Army of Darkness" name, while games like Evil Dead: Fistful of Boomstick and Evil Dead: Regeneration do reference these other characters by name. I'm certain this has more to do with copyright than anything else, but that's all the more proof that these characters are not considered "Canon" in the Army of Darkness continuity.
Ash vs. Evil Dead contains references to all three of these timelines, though, and I think we can probably assume that (with the exception of non-canon video games and comics) the continuities have all been merged, due to Bruce referencing spending the night with "some friends" at a cabin, and not just his girlfriend (meaning the events of Evil Dead 1 are canon now), and due to Bruce not having his hand OR any prosthetic (Evil Dead 2) and of course, his use of the word "Boomstick" (Army of Darkness).
So the timelines have converged for the new show! Anyway, that's my time paradox explanation. It's probably completely BS, but I think it's unique and explains everything better than any other theory I've come across without reaching too much.