Hi @huckleberry,
First off, nice site! The colors are really great. 🙂
The thing about tickets is that they themselves are a Products custom post type in WooCommerce, so they will not necessarily expire in the product catalog once an event has ended–but rather once the quantity has been depleted.
To hide them from the catalog, edit the ticket in the WordPress editor (Products > Products > Edit Product), then select the “Hidden” option in the Catalog Visibility settings (screenshot). That will effectively remove the ticket from showing up with the rest of the products in the catalog.
Cheers!
Geoff