Kaporos origin

The Armenians practice "matagh", where they slaughter a bull, lamb, dove or rooster at the door of the church. It is believed to be based on pre-Christian syncretism. Note that the rooster is the only option which is not used for sacrifice in Judaism. It is important that kaporos not be viewed as a sacrifice outside of Yerushalayim.

The purpose of matagh is to give a gift to G-d and as charity to the poor. It is also eaten on the day it is slaughtered. Is that why we would do it on erev Yom Kippur, so there was no opportunity to leave it over? Think pre-refrigeration. The Sephardic masters claimed that kaporos with a chicken was based on idol worship and the mishnah decrees that it is improper to sell a white rooster to an idol worshipper, except in a bulk context. The custom had died out until it was revived by the school of the Arizal, which immersed itself in "kabalah", though it is unclear to the earlier Sephardim that this particular custom came from any known place in kabalah.

Is the origin of matagh the source for kaporos as well?