Midrash Eleh Ezkerah is a dramatized narrative describing (with poetic license) the tragic executions of ten of Israel’s greatest sages at the hands of the Romans. The story depicts these ten as having lived contemporaneously and having been executed more or less in the same time and place, though this was not actually the case.
Nevertheless, in this work, the body of the sage Rabbi Akiva is carried by Elijah the Prophet. Elijah meets Rabbi Yehoshua haGarsi, who asks Elijah how he could carry Akiva’s dead body when Elijah is a Kohen, and a Kohen is forbidden to come into contact with a dead body, lest he become tamei — spiritually contaminated. Elijah replies, “The bodies of the righteous do not render spiritual contamination.”
It appears that the author of this narrative was of the opinion that Elijah was a Kohen, and therefore would line up with the opinion that Elijah was in fact Pinchas.