Is there such a thing as "open" double-blind peer review?
Yes, there is such a thing as "open double-blind" reviewing: the "Frontiers in" journal series uses exactly this model.

During the review process, "control" is handed back and forth between editors, reviewers, and authors in an incremental "conversation" model, in which the paper might go through many incremental revisions.  If the editor determines the paper cannot proceed or an author is unable to reply to reviewer comments, then it is rejected.  Otherwise, reviewers, once satisfied with the paper, sign off with an endorsement.  When all reviewers have endorsed, the paper proceeds to publication and the identity of the reviewers is revealed on the final published version.