The main editor would be able to do this, although it could introduce problems if not tracked carefully.
When an article hits the "unassigned" queue, the editor can click the "Edit Metadata" link and change the author's first and last name and email address. These fields can't be completely blank, so something will have to be added there; in addition, if you change the email address, system emails won't work as expected. Normally, you'll have the option to edit/add the email address for any correspondence between the author and editor, but again this would be adding a certain layer of complexity to the arrangement. As well, the editor would have to re-add their names before publication, otherwise you'll be getting some very strange results in your ToC.
I would suggest trying that; also, what you may want to try is adding the four editors as reviewers, and sending the content-stripped papers to them for a preliminary review round. They could then simply use the review comment box to suggest the reviewers to be chosen for the next review round. They wouldn't have so much in the way of hands-on control, and it would again add a layer of complexity for the main editor, but it would guarantee they see the papers blind.