FWIW, my H&R 'Buck barrel, a smooth 12ga., has open sights. It shoots slugs to them quite well and, surprise to me, snap shooting with shot goes pretty much where Im looking. The front sight is not just a bead, but a tallish blade. It works so well I havent put the old bird barrel back on, its my 'all rounder' as is.
Even so, each barrel is its own self, so yours may not do as well for you. I would have tried the peep myself if it was already D/T'ed. You could anneal a piece of hacksaw blade and use the hole for the peep, put a bend in it and epoxy it on to try out the idea.