Hi Justin,
That is actually the correct behavior when you choosing single event category layout. It will display the recent post and statistic of the event category.
Perhaps you can try this method if you want to display the event listing in single category.
Login to your backend->Menu->Main Menu->Add New Menu Item.
In Menu item type->Select
http://screen.stackideas.com/menu_cat_1.png
Select System Links->External URL
http://screen.stackideas.com/menu_cat_2.png
Go to your frontend and go to the event listing inside the particular category from the event listing page. Copy the url and go to the next step.
Select Link->Copy the link of the list of events for that particular category and past it on the text box
http://screen.stackideas.com/menu_cat_3.png
Click Save button
http://screen.stackideas.com/menu_cat_4.png
After you have setup the menu, login to your front end, you will be able to see the menu linking to the list of events for that category.
http://screen.stackideas.com/menu_cat_5.png
Hope that helps
Best regards
Chris