Now you've done it. You've found a Point of Divergence that radically changes the course of history. Congratulations; you should feel good. Especially when you look at the work load you've imposed on yourself.
Everything you know about the world is wrong. There are generations of people who were never born. Entire populations' worth of cultures and politics to design from scratch. How are you supposed to contain this? With the judicious use of Butterfly Nets.
Butterfly Nets are self-imposed restrictions on how far and fast Butterflies are allowed to spread. Just put them up, and you won't need to wonder about how your PoD affects things like tiny little kingdoms in Southeast Asia you've never heard about, or Papal successions, or whatever. Beyond the Butterfly Nets, you can simply assume that the changes caused by your ATL haven't had an impact yet, and history is allowed to evolve convergently. Is it simple? Yes! Is it elegant? Yes!
But is it plausible?
Somewhat so, actually. Butterfly Nets can be pretty plausible, as long as you're very clear on how far they extend and how long they last. If you're writing a medieval European ATL, almost everybody will give you a free pass to set up Butterfly Nets around the New World. (At least until it gets discovered.) Once the changes start interacting with the world beyond, though, the famous people start increasingly turning into recognizable people In Name Only, and keeping the Butterfly Nets up becomes less plausible (and much harder) than letting them fall.