Overlapping episcopates did not come to England until, I believe, the Acts of Toleration which allowed the Pope to send priests and bishops of his own to care for the Roman Catholics in the country (although the priests had been there in an underground fashion for quite awhile). The Act of Supremacy and the Elizabethan Settlements simply disconnected the existing episcopacy (which had been in place for many centuries) from the Papacy.
In Quebec, the Catholic Church operates and English diocese and a French diocese- overlapped.
Do you happen to know offhand whether the papacy formally dissolved and suspended the Catholic dioceses in the interim, or did the Vatican establish an episcopacy in exile of some sort?