How to get a task list from “Assign a Task” on the Document Set Welcome Page

Question

We are about to upgrade to SharePoint Online but all workflows must be upgraded to 2013 before they will migrate.

In the past the SP2010 Approval Flow process, I could crack open and add a Document Approval Log (for capturing comments) and set a DocSetID at both the DocSet, DocAppLog and Task List.

In SP2013, I am forced to switch to "Assign A Task," and it doesn't have the same flexibility. Finding a common field to update list item (DocSetID) has proven futile. I can't get it to update - the only common field seems to be Due Date for Tasks and Title for my Approval Log.

I've researched several solutions but either my environment isn't set up the same (Special Lookup field) or anything I have tried hasn't worked.

Any insight would be appreciated.