I'm a smidge confused . . . "eggs in stuffing" in my childhood-family-realm meant chopped-hard-boiled-bits mixed in with the stale bread / et.al. stuff.
my fav is Pepperidge Farm - with diced onion + celery + mushroom added - using a not-specified stick/115g butter melted in the (usually) chicken broth liquid add.
it is pretty 'sticky' - not sure how an egg binder would help....