I copied the DB because of the extensive changes and the indexes were not brought over properly. This slowed the biggest table down. Removing the derived step helped me figure out that it was further down the line, despite the fact that monitoring the SSIS execution of the data flow made it seem as thought it was the derived step.
I realize this is probably not going to happen often, but I'll leave the thread here in case anyone else has the problem and mistakenly identifies it like I did!