As there noted, with (only) certain types of predicates, a reflexive object in a complement clause is possible anteceded by a main clause subject:
For me, iii lacks even a hint of any reading in which himself is not anteceded by Peter.
The latter would be anteceded by the main clause subject and serve as the clause-internal antecedent of the (non-LDA) reflexive.
This was a pagan priesthood, not a Jewish one, and it may have anteceded
the Jewish priesthood, because the Jewish people did not exist until after their liberation from Egypt.