Modernize Phame process handlers
Summary: Converts Phame to use handleRequest where appropriate.
Test Plan: Write some blog posts, publish, edit, view.
Reviewers: btrahan, epriestley
Reviewed By: epriestley
Subscribers: epriestley, Korvin
Maniphest Tasks: T8628
Differential Revision: https://secure.phabricator.com/D13677