I see that the Jews here were seeking Him for the wrong reason:
Because they had their stomachs filled, and not because they recognized their need of Him spiritually or because they saw the miracles and believed on Him.
He is answering them according to what He says further down in John 6:63:
" It is the spirit that quickeneth; the flesh profiteth nothing: the words that I speak unto you, [they] are spirit, and [they] are life."
The words the Lord was speaking to them were spiritual, not carnal.
As His people, it is the Spirit that makes one alive, while the flesh profits us nothing.
Also, based on what He tells them later on in John 8:43-47, they ( for the most part ) did not hear Him, because they were not "of God";
Therefore, because they were not "of God" ( His sheep ) and were asking Him questions whose answers they would not accept or even understand, I see that they asked Him the wrong question in John 6:28.
He tells them in the previous verse not to labor for the "meat" that perishes, but for that which endures to everlasting life...which He would give them.
When they ask Him, "... What shall we do, that we might work the works of God?", they asked Him how they could do God's work...
But only God can do God's work.
We as men cannot do God's work unless He does those things through us ( see Philippians 2:13 ).
So, Jesus is not telling them how to do God's works in John 6:29, but that it is the work "of God" for someone to believe on Christ:
" Jesus answered and said unto them, This is the work of God, that ye believe on him whom he hath sent."
This agrees with the many passages that tell us that the Lord chooses someone and causes them to approach Him ( Psalms 65:4 ), that it is given to them to believe ( Philippians 1:29 ), that faith is a gift ( Ephesians 2:8 ), and that He opens the heart so that someone will listen to His words ( Acts of the Apostles 16:14 ).
Again, you and I see this passage ( as well as many others ) very differently, as we ( undoubtedly ) see all of John 6 very differently.
Because of this, I feel that we must agree to disagree, and leave it at that.
That said, I wish you well, sir.
May the Lord bless you with both wisdom and knowledge, as well as many good and perfect gifts.