Webform Event Registration skips payment processing
I was able to get this working by recreating the form using 7.x-4.12 version of the Webform CiviCRM Integration module. (Simply upgrading the module and using the existing form would not work.)

In addition, I had to make sure that Webform>Payment Processor had both "Pay Later" and "Credit Card or PayPal" selected. (You'll notice on the screenshot above that only "Pay Later" displays.)