Slightly improve organization of PhabricatorApplicationEditEngine

Summary: Ref T9132. This just moves code around, breaks it up into some smaller chunks, tries to reduce duplication, and adds a touch of documentation.

Test Plan: Created and edited pastes.

Reviewers: chad

Reviewed By: chad

Maniphest Tasks: T9132

Differential Revision: https://secure.phabricator.com/D14398