Hi, Luke.
You can go to the top-right corner of the wp-admin event edit screen, click “Screen Options”, and then check the “Author” box.
Then you can do the same when editing the other two post types (organizers and venues).
From then on, you’ll have the Author drop-down available when editing one of these three post types.
As far as custom permissions/capabilities go, you could use a plugin like User Role Editor (third-party, not guaranteed or supported by us) or one like it or custom coding. In other words, it’s not something we support.
If you need some coding help, you may want to ask your developer or reference our documentation and list of known customizers.
Please let me know if you have any follow-up questions on this topic.