They needed a big, attention grabbing event with lasting changed regardless. But I'd prefer if the event happened without altering continuity. Just play it off as an epic event that killed off some big name characters like Barry and Kara, and set up new overhauls for the big name books. Leave the Multiverse intact, because I don't think the Multiverse was ever actually a source of confusion for readers. It was more that DC's writing style was corny and outdated for the most part compared to Marvel, and that didn't need a continuity re-set to fix.
So put Byrne on Superman and Perez on Wonder Woman, but don't have them do a continuity reboot. None of their big changes really required a reboot to happen anyway: Lex can just shift gears and try to be a "legitimate" businessman, Clark's relationship with Lois can evolve, Kara is dead anyway so why go the extra step of wiping out her entire existence, etc. Diana just needs to drop her secret ID and get a power upgrade so she has full flight; the mythological elements already got some serious attention in NTT, so Perez could have overhauled them further within the confines of continuity. New cast like the Kapatelis women and Myndi? So what, just add them onto the ever changing status quos Wonder Woman had any way. Same with the villain revamps. Barbara Minerva is the third Cheetah in publication history, might as well just have it be reflected in-universe as well. And there wouldn't be the domino effects all of this had on the Legion, Justice League and Donna.
Alternatively, if there is meant to be a reboot no matter what? Don't screw around and try to have it both ways. Just hit the re-set button across the board. Have the Earths be merged in the story to stop the Anti-Monitor, and then un-merge them when he is defeated. And from that event, a new Earth is created from their merger that combined aspects of all of them. This New Earth would be the focus of all ongoing stories: new iterations of Superman, Batman, Wonder Woman, etc. with all new histories. The classic Earths would be understood to still be existing, but they wouldn't be touched upon anymore.