There is just one problem, Sproul never clarifies or even give us any context at all to his statements. That user is right to observe this too. You cant just say there's some context we missed if nothing is linguistically indicated or that no clarifications and explanations is given. He just flat out states the Second Person of the Trinity didnt die or didnt make Atonement. If he wanted to say as you said, then Sproul should had said that "it is not in His Divinity Jesus Christ died, but in His humanity, He, the Second Person of the Trinity died". Boom! this easily clarifies what he means and wouldnt raise any eyebrows. Unfortunately Sproul never did that nor even make any disclaimer or further clarifications.
Asking the question of whether Mary gave birth to divine flesh doesnt help clear Sproul's name, as for one eventhough Jesus' human nature is like us in every respect except sin, guess what does Cyril says about the flesh of Christ. It's life giving and is given in the Eucharist in the bread and wine. He even says that Christ's humanity is also deified and who denies this? Nestorius!
Of course had you meant flesh which is by definition immutable, immaterial, omnipotent…etc, then yes that is of course not the case at all, but it doesnt add anything as Nestorius surely didnt have worries over Theotokos over this, it was that the term implies Mary birthed the Godhead as Cyril explains in his "Against Nestorius" at the beginning. That does not answer anything because no one believes that.
Next, you shown yourself to employ Nestorian Prosophic reasoning to Christ. The humanity is united to the Divinity in the person of Christ. They arent two independent natures. They are distinct and retain their intergrities which is how the natures arent confused with one another. Years before the Christological Controversy, Irenaeus shown how there can be a 'mixture' of humanity and divinity in Christ through Stoic mixture theory which explicitly states two substances retain their intergrities, composition and doesnt mesh into some hybrid. In that state however, the two arent "independent". To say they are goes against Cyril's Christology and the importance of deification of the human nature.
Of course it isnt in His Divinity a Divine person experiences pain but it is in the assumed humanity. However a Divine person is still the subject that perceives the pain! Hence you cannot say "a man Jesus Christ died". That's following the Prosophic theory of Nestorius as Mcguckin shows and implies that it isnt the Logos who is the subject that is hunged on the Cross.
Also what "natures" is are a set of attributes an agent or thing has, it isnt the thing itself but properties belonging to an agent or a thing. A set of attributes didnt die or atone for sins, but an agent or subject who has these set of attributes do. To appeal to their tangibility wont work either, as when someone dies, nobody says the human nature of the someone dies or gets extinguished but that the person dies!
When a pig dies, we dont say "four hooves, a snout, two ears, oinks, tail, pink, hairy, fatty" died, we say a pig which is the subject, dies.