Clean up EditEngine implementation on Badges
Summary: Fixes T10672. Cleaning this up myself since I was responsible for the implementation.
Test Plan: Leave a comment, Edit a badge, create a badge.
Reviewers: lpriestley, epriestley
Reviewed By: epriestley
Subscribers: Korvin
Maniphest Tasks: T10672
Differential Revision: https://secure.phabricator.com/D15556