Sometimes we just have to hold our hands up and admit "it's tricky"!
"Great is the mystery of godliness (or "Great is the mystery of our religion of godliness" ?) - God was manifest in the flesh".
God came as close to tasting death as it is possible.
Jesus Christ was and is both man and God.. it isn't always helpful to separate Him into two natures... He was and is one person.. and as one person he was and is the Son of God. And as one person he died for our sins. And as a person, he was loved by the Father. The Father did not only love his divine nature but not his human nature, or say "You are the Son of God merely because you have the divine nature." From the moment the Son of God became incarnate adding a human nature He became the Son of God in his entire person.
When anyone is experiencing the physical pain of dying the only reason they feel the pain is because their body is united to their spirit. As soon as the spirit leaves the body the pain of dying ceases.
Is it not, then, the body that gives the pain and the spirit which receives the pain?
Perhaps such a thought is not correct, but we cannot just assume that Jesus in his divine nature did not taste the pain of death, even though he, in his divine nature, did not actually die.
We experience the pain of death even though at death we, that is our spirits, are still alive.
Is there then any really significant difference between our Lord dying and the death of a believer whose spirit goes to glory upon death, awaiting the resurrection of the body... excepting, of course, that he died not for his own sins but for ours that we might live, and that he experienced all that punishment the scale of which we cannot begin to fathom for all the sins of all his people?