Hey there, James! Welcome back to the forums. 🙂
Man, sorry you have to go through the process of a clean install–I know that’s never fun.
The good news is that you can do a straight export from WordPress under Tools > Export. Events, Venues and Organizers are separate post types, so make sure each one of those is exported and then import those into your fresh install. That should get you covered.
Those posts are saved to the wp_posts table, so they would be included along with the rest of the posts on your site, if you wanted to go the SQL route. 🙂
Does this help? Please let me know.
Cheers!
Geoff