Very well, although that way you are still likely to "discover" allegory simply because it becomes an easier explanation. Sort of like some see in the feeding of the thousands by five loaves a figure of human economic cooperation.
in private he is always explaining the analogies, just as happened in John 6
So you discard the plain reading of "food indeed" in favor of the imagined private explanation not recorded anywhere in the Scripture. If that is your hermeneutic, why do we need the Bible?
We see what Christ explained privately to St. Paul. He taught him to teach others to "discern the body". We also see the written text of the speech at the Last supper: "this is my body, which is given for you". No room to imagine allegories privately explained.
analogy is the default delivery mode for Jesus public teaching ministry
I think I responded. When He tells a parable He usually makes it clear it is a parable. There is a difference between teaching by parable and teaching by parable never explaining that it is a parable. When the parable is not delineated in the text, like with Jesus "the door", that is because it is impossible to take it otherwise: the disciples in it become "sheep", Jesus stops being a door and becomes shepherd, there are wolves involved, then He is vine and we are branches... it is impossible to take literally, it becomes a children's theater with dress-up.
With John 6 we either have a teacher who drives his disciples away for the sake of telling an offensive to them parable and still does not explain the truth after the parable failed -- or we have what the Bible says without hidden meanings.
But Peter believed, right then and there, that Jesus was Messiah, the Son of the Living God. Peter through faith, right then and there, had the vital nourishing connection to Christ that is implied in John 6:63, My words are spirit, and they are life. When Jesus says I am the bread of life: he that cometh to me shall never hunger; and he that believeth on me shall never thirst., that is literally fulfilled by Peter and the Apostles believing in Him, trusting in Him and His mediatorial work for their salvation, right then and there.
Yes, the Apostles believed before the institution of the Eucharist, because Jesus was present in the flesh for them. He would not be in the flesh for us if not the the Eucharist; and so Christ gave us His body in perpetuity. It is a part of the deposit of faith that the Church received.
If I don't seem to respond, please ask again. My time dedicated for this is limited and I may overlook a point, or consider it unimportant, or simply not respond because I agree with you on that point.