You don't need to change the mapping in the restlet router to match the new pattern "restlet/*" because the restlet router will now be considering "example.com/restlet/" as the base url.
So, if you change the router to match "/restlet/doSomething", your actual url will be "example.com/restlet/restlet/doSomething", which obviously will not work.
So, change your restlet routing to:
router.attach("/doSomething",DoSomething.class);