On SingleUserAuthorizer, don't call Authorize. Also, any time you provide all 4 credentials to any authorizer, you don't need to call Authoirize. LINQ to Twitter will use those credentials to build the authorization header.
The case where you would call authorize is if you only provided ConsumerKey and ConsumerSecret and the authorizer type is not SingleUserAuthorizer. Authorize implements the part of the OAuth protocol that gets the OAuthToken and AccessToken.
Your syntax for SingleUserAuthorizer should work, but here's another way that matches keys to how the Twitter app page names them:
var auth = new SingleUserAuthorizer
{
Credentials = new SingleUserInMemoryCredentials
{
ConsumerKey = ConfigurationManager.AppSettings["twitterConsumerKey"],
ConsumerSecret = ConfigurationManager.AppSettings["twitterConsumerSecret"],
TwitterAccessToken = ConfigurationManager.AppSettings["twitterAccessToken"],
TwitterAccessTokenSecret = ConfigurationManager.AppSettings["twitterAccessTokenSecret"]
}
};