Unless something's changed very recently, you cannot exchange a WDW ticket for a DL ticket at the ticket booth. It can only be done at the entry turnstile. I've done it, and it shouldn't take 15 minutes. Maybe 5, I'd say. The CM at the turnstile pushes a button somewhere and another CM magically appears to get your ticket, takes it away somewhere to scan a day off of it, and then returns with it. While the 2nd CM is away with your ticket, you'll sort of stand off to the side a bit while the first CM processes other people entering the park. When your ticket is returned, the turnstile CM will issue you another park ticket to use in the fastpass machines for the day. Hope that makes sense!