I think the idea of these two murders being unconnected is improbable.
However it is not improbable they could have been commuted by a different murderer.
If the cry went up from Berner Street "The Ripper's struck again" and Jack is out having a quiet pint, he finished his pint leaves the pub and while the police are running in the opposite direction he finds a woman walking alone, still a bit worse for drink and they agree to some business in a dark corner of mitre square.
Two murders, by different hands, but the later inspired by the former.
My opinion is all I have to offer here,
Smilies are canned laughter.