Do you also know that John is the only gospel that DOES NOT mention the institution of the eucharist during the Upper Room Discourse (John 13-17)?
John 6 is at best ... a foreshadowing of the 'sacrament' ... but for John to omit the institution in chapters 13-17 wrecks your whole exegesis.
I tend to treat the 4 Gospels as a bunch, so no difficulty at all in attributing sacramental presence in any case. Exegesis? All I did was pull text. You apparently inflicted some “exegesis” of your own.