You ARE aware that John 6 took place after the feeding of the 5000, and not at Passover? Why do you read the Lord’s Supper into what happened long before it, and ignore what Jesus said DURING His institution of the Lord’s Supper:
This is My body which is given for you; do this in remembrance of Me.
John chapter 6 DOES contain some good stuff; don't it!!
Jesus answered, The work of God is this: to believe in the one he has sent.