I have to come back to this:
Turns out that the user who owns the events I need to display also owns events for other organizers, but there is no organizer filter for the User Owned Events endpoint.
It appears that the only way I can display all public events ( live or started) for an organizer regardless of ticket status (= produce the same list people see when they go to the organizer page) is to download all live or started events for the user and then filter out the ones for the relevant organizer on my end.
This doesn't really make sense to me. Producing that list seems to be a common task, I assume. Also hiding sold out events from the search doesn't make sense to me. We would still always want to display these events, indicate that they are taking place and provide details. The fact that they are sold out is a different matter...