You said:
“Catholics jump on John 6 to establish the authenticity of the Eucharist as the literal flesh and blood of Jesus, but back away from John 6 regarding its sufficiency for salvation and even its necessity for salvation.”
I don’t know where you get this idea. Catholics have always believed in the Holy Eucharist as the source and summit of Grace, because we receive Him into ourselves. Because Jesus is the Paschal Lamb, He is required to be consumed in order for us to enter into the New Covenant with God. (see St. Paul’s teaching in 1 Corinthians 5:7-8)
Jesus makes it quite clear in John 6:
Verily, verily, I say unto you, He that believeth on me hath everlasting life. I am that bread of life. (vs. 47-48)
Your fathers did eat manna in the wilderness, and are dead. This is the bread which cometh down from heaven, that a man may eat thereof, and not die. I am the living bread which came down from heaven: if any man eat of this bread, he shall live for ever: and the bread that I will give is my flesh, which I will give for the life of the world. (vs. 49-51)
Then Jesus said unto them, Verily, verily, I say unto you, Except ye eat the flesh of the Son of man, and drink his blood, ye have no life in you. (vs. 53)
Whoso eateth my flesh, and drinketh my blood, hath eternal life; and I will raise him up at the last day. (vs. 54)
For my flesh is meat indeed, and my blood is drink indeed. He that eateth my flesh, and drinketh my blood, dwelleth in me, and I in him. (vs. 55-56)
As the living Father hath sent me, and I live by the Father: so he that eateth me, even he shall live by me. (vs. 57)
This is that bread which came down from heaven: not as your fathers did eat manna, and are dead: he that eateth of this bread shall live for ever. (vs. 58)
In the above verses, Jesus says seven times that if we eat Him, we will live in Him now and/or have everlasting life later. It can’t be any clearer than that.
You also said: “I agree with you that taking the Catholic Eucharist is neither necessary nor sufficient for salvation.” I most assuredly did NOT say that and I don’t appreciate your attributing something to me that is entirely false!
If you are going to post on what the Catholic Church believes, I would respectfully request that you read the “Catechism of the Catholic Church” so that you can post accurate facts. Please do not make up things about Catholic beliefs.