How could Christ’s deity not have died on the cross?

I don’t know of contemporary Adventist sources that comment on this concept, though there may indeed be some. I think we are simply dealing with one of the mysteries of the Incarnation. Jesus was fully God and fully human, with His two natures blended into one. I found more of the statements you quoted in this reference from The Seventh-day Adventist Bible Commentary, (5:1113, 1114) in the “E. G. White Comments” on Mark 16:6: 6 (John 1:1-3, 14; Phil. 2:5-8; Col. 2:9; Heb. 1:6, 8; 2:14-17; Hebrews 4:15). Deity Did Not Die.—Was the human nature of the Son of Mary changed into the divine nature of the Son of God? No; the two natures were mysteriously blended in one person—the man Christ Jesus. In Him dwelt all the fullness of the Godhead bodily. When Christ was crucified, it was His human nature that died. Deity did not sink and die; that would have been impossible. Christ, the sinless One, will save every son and daughter of Adam who accepts the salvation proffered them, consenting to become the children of God. The Saviour has purchased the fallen race with His own blood.

This is a great mystery, a mystery that will not be fully, completely understood in all its greatness until the translation of the redeemed shall take place. Then the power and greatness and efficacy of the gift of God to man will be understood. But the enemy is determined that this gift shall be so mystified that it will become as nothingness (Letter 280, 1904). . . .

“I am the resurrection, and the life.” He who had said, “I lay down my life, that I might take it again,” came forth from the grave to life that was in Himself. Humanity died: divinity did not die. In His divinity, Christ possessed the power to break the bonds of death. He declares that He has life in Himself to quicken whom He will.

All created beings live by the will and power of God. They are recipients of the life of the Son of God. However able and talented, however large their capacities, they are replenished with life from the Source of all life. He is the spring, the fountain, of life. Only He who alone hath immortality, dwelling in light and life, could say, “I have power to lay down my life, and I have power to take it again.” . . .

Christ was invested with the right to give immortality. The life which He had laid down in humanity, He again took up and gave to humanity. “I am come,” He says, “that they might have life, and that they might have it more abundantly” (YI Aug. 4, 1898).

If God is by definition immortal, how can deity die? As Mrs. White said, “That would have been impossible.” Yet Jesus died, and His death affected even His divinity. It did not die, but it was at least quiescent in the tomb. I don’t understand all this, but I believe that something along this line must have happened. Perhaps this will be one of the themes of salvation that we will contemplate for eternity.