In John 6:47-58 Jesus compared himself to the manna that the Israelites feed on to sustain their physical lives and yet died by saying he was the bread that if one fed on would not die.
How to “feed” on that “bread”? Vs. 47 says by exercising faith in Jesus and his sacrifice. As Paul said, Christ entered into a “holy place with his own blood”, into heaven.
Just as the physical bread sustained a person’s life that “bread from heaven”, Christ, would give everlasting life. The bread represented his flesh.
On our reading, the words of the Last Supper answer the conundrum of John 6, which the Jews found a "hard saying." On your reading, the words of the Last Supper are at best badly phrased.
Again, how does comparing (if you must) the bread to Christ's body ("which will be given up for you") say something about or illuminate the bread other than by taking Christ at His word?