You are cherry picking words from a verse that doesn't speak toward renewing.I Think we have hit the nail on the head of where you and i differ.
Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind. (Matthew 22:37)
Renewing of the heart is when the believer begins to walk in the Spirit...
The renewing that Scripture speaks of is renewing the mind.
In the verse you are quoting, Jesus speak of loving God with your heart, soul and mind. If you were being consistent you'd be speaking of renewing the soul also, but I expect you leave it out since it doesn't serve your purpose and you realize it would be indefensible.
Simply because you can find a passage that uses those words doesn't give you the authority to change around such plainly worded Scripture, such as,
Romans 12:2 KJV
2) And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God.
Ephesians 4:23 KJV
23) And be renewed in the spirit of your mind;
Colossians 3:10 KJV
10) And have put on the new man, which is renewed in knowledge after the image of him that created him:
Much love!