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.
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Bartosz Dziewoński