Not sure I understand your questions.
I don't believe Christ had a carnal nature.
To believe Christ had a carnal nature implies that He had sin, which is worse than what the pope just said.
I've been in churches where some believed Christ was exactly like us -- the discussions got quite heated, and very evident that they wanted a Christ who had a lot of sin inside himself that He needed to overcome. Of course they claimed that the sin never manifested itself in actions, therefore they still claimed they believed Christ never sinned. However, their idea of a sinless Saviour was totally destroyed by their insistence that He had all this sin inside Himself in the same way humans have sin inside.
By dragging Christ down to our level of "sinful nature" people can then elevate their own righteousness, saying, well Christ had to battle this tendency as well, so I don't feel so bad about it.
When we drag Christ down to our level, we drag down the standard. Then we see in Christ a man struggling against sin, not a perfect life.
Christ didn't have to be "born again" -- He didn't have to overcome a carnal nature. He abhorred sin, it pained Him. He had the spiritual nature from the beginning.
I agree with you that our "overcoming" is but a faint shadow of the perfection of Christ.
There are three natures --
1.The carnal nature, the nature at enmity against God and His law.
2.The natural human nature, the human nature with legitimate needs and desires, that aren't sinful in themselves, but can become sinful.
3.The spiritual nature, which comes only when a person is in connection with God.
We are born with both a natural and carnal nature.
Our carnal state turns our natural needs and desires into sinful thoughts and actions. We must be born again, of the Spirit, to newness of life, only then can we even begin the spiritual walk.
Christ was born with both a natural and spiritual nature.
His spiritual nature, always in connection with His Father, kept his natural human needs and desires under the will of Father, at all times.
There is a dual nature here, Christ's spiritual nature is sinless, yet he takes on human FLESH with all the consequences that sin has wrecked on the human body. His spiritual nature does not possess the evil passions common to the carnal, sinful nature. The carnal nature is compatible to evil, Christ's spiritual nature recoils from evil.
How then can He be tempted in all points as we are?
-- He was tempted FAR MORE than we are.
Sin, when broken down to it's basic reality, is basically the desire to be our own "gods". It is defying God's authority, and doing what we please.
Christ took humanity, and it was agreed in the councils of God, that He would live as a human and not use His Divinity, but place Himself totally under the will of the Father and do only that which the Father commissioned Him to do.
RH.1875-04-01
It was a difficult task for the Prince of Life to carry out the plan which he had undertaken for the salvation of man, in clothing his divinity with humanity. He had received honor in the heavenly courts, and was familiar with absolute power. It was as difficult for him to keep the level of humanity as it is for men to rise above the low level of their depraved natures, and be partakers of the divine nature.
Christ was put to the closest test, requiring the strength of all his faculties to resist the inclination when in danger, to use his power to deliver himself from peril, and triumph over the power of the prince of darkness. Satan showed his knowledge of the weak points of the human heart, and put forth his utmost power to take advantage of the weakness of the humanity which Christ had assumed in order to overcome his temptations on man's account.
Satan's temptations to Jesus was to try and get Jesus to step out of that role.
He does the same with us -- though for us it's kind of silly for us to think we can be our own "god". But for Christ, it was NOT silly. He WAS GOD, fully divine.
But He must put aside His former power and glory, and live as a man, doing the will of the Father in heaven.