I’ve wondered the same as you about the John 6:66 verse.
Could be right about it (though I don’t see it as those rejecting the eucharist, but rather rejecting His salvation (this body which is broken for you, this blood which is shed.....eat and drink meaning to partake of the salvation and deliverance of Jesus Christ, being born again, born of the Spirit).
As a Catholic, I would take it more literally that it means to eat the Eucharist, but by implication, that would also mean everything implied in the Eucharist: along the lines of what you said, this is a life of faith, hope and charity through Christ by the grace of God, by which we may merit Heaven as adopted Sons and Daughters of the Lord.
That’s exactly what it means. I once heard a joke about christians coming to Heaven and when St. Peter greets them, they ask him what that line over there is. He says, “Shhh, those are Catholics. They think they’re the only ones here.” This mirrors that joke. I truly hope the joke’s not on them if they think the Eucharist will save them.