I see you've already solved your problem - but for posterity:
We had a similar problem, and the SVC handler was already correctly installed. Our problem was the ExtensionlessUrl handler processing requests before they reached the SVC handler.
To check this - in Handler Mappings in IIS Manager at the web server level, view the list of handlers in order (it's an option on the right-hand side). If the various ExtensionlessUrl handlers appear above the SVC handlers, then repeatedly move them down until they're at the bottom.