Something I realized regarding the green ring–it’s to bring BOB back to the Black Lodge, not the doppelganger. Ray’s mission was to kill the Bad Dale and put the ring on him to return his corpse, and thus BOB, to the Lodge. Presumably this is what MIKE wants the good Dale to do, as well. Ray was operating under Phillip Jeffries’s orders (who possibly works for the Fireman) but I think it’s safe to assume that both Lodges want BOB to return to the Black Lodge.
Hell, that adds another meaning to “The Return” title as well.