It turns out that it is relatively easy, as long as you remember one thing that Facebook does not mention:
Use Facebook as your personal you!
Summarizing all steps:
- Use the full desktop interface, no app
- Create the event, published or not
- Make sure to use Facebook as your personal you: click the down triangle at the top right and click your human name, not the Page's name
- Find the event
- Edit it
- At Co-Hosts, add any person you know managing the other Page
- Ask that person to follow the same steps (instead of creating the event s/he should attend it)
- Ask that person to add the other Page as co-host
The event will now automatically be shown on the other Page's list of events. Anyone managing the other Page can now invite their fans.
Both Pages will be shown as organizers, at least sometimes. In some situations however, only the 'relevant' Page is shown: the one the user happens to like.
Note that Page events can have persons as co-hosts, but not the other way around: personal events can only have persons as co-hosts.