I think your plan sounds basically sane. I don't think there's anything that would do the work for you, but you might want to look at the source code of https://www.mediawiki.org/wiki/Extension:UserMerge to confirm your list of tables that store user ids and will need updates.
Note that various extensions also have their own tables and also store user ids, the UserMerge extension has some hooks to make it possible to update their data.