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