From your perspective, you don't find it extraordinary that John felt the need to "instruct" about the Last Supper in John 6 but then does not even mention it during the events which surround the passion? The Upper Room Discourse? I think you have to look for another explanation for John 6, the symbolism does not fit the context or the later developements of the book.
You need to look at the last sentence — might be verse 59 or the one after it.
“And one of you is a devil.” Christ doesn’t name Judas personally, but John refers to Judas more than any other Gospel.
Yes, there is a tie to the Last Supper.
Do you understand the statement that I used above? John was writing theology for the people of his day, not a historal synoptic Gospel, but theology. There are so many levels of meaning when you do a Bible Study of John.