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... ...
You have answered your own question already. There is a distinction between the eternal Son and the human incarnation, Jesus. The eternal son does not have a fleshly body. The human body died. The eternal spirit cannot die. Our bodies will die some day while our spirits live forever.