django 1.7 migrations — how do I clear all migrations and start over from scratch?

So the step-by-step plan I outlined in my question does work, but instead of deleting rows from the south_migrationhistory database table, I had to delete rows from the django_migrations database table.

The command is: DELETE FROM django_migrations WHERE app='my_app'

Once this is done, you will be able to re-run your migrations from scratch.