Most all Pauline scholars assume he was on foot, since only Romans maintained a stable, but it's Ok if you would like to provide him with a camel. 
Poiein, however, in all my dictionaries means simply to do or to act. It never literally means "offer up." The OT citation is as you say "offer up," because the entire context is about providing a sacrifice. Still, it is a stretch to lift that meaning into a quite different context. All the translations I have seen simply say "Do this in memory of me," without any mention of priests  or priesthood. Perhaps you are being exegetically adventurous?
Who ever said that the church emerged from the catacombs?