I consider timelessness a necessary property of God, but it seems to conflict with the Incarnation. Can anyone offer any ideas of how this might be resolved?
There are two main conflicts that I see: we have one member of the Trinity being separated from the other two (John 14:28; 16:28; 17:5; 20:17) and being, if I am reading Philippians 2:5-7 correctly, changed somehow himself; and we have a timeless person experiencing changing mental states. Timelessness precludes change, so from the Biblical data, how is it possible for Jesus to be a timeless person incarnate?
The Second Person of the Trinity, the Son, was never “separated” from the other two Persons of the Trinity - in the sense that after the incarnation there were only two Persons present in the one God; or that there were then two Gods (one consisting of One Person, the Son; the other consisting of Two Persons, the Father and the Holy Spirit.)
Within the Triune God however, the Three Persons are distinct from each other.
You may find paragraphs 249-260 in the Catechism of the Catholic Church helpful regarding Catholic Trinitarian dogma.
Regarding the Incarnation:
*Phil. 2:5 Have this mind among yourselves, which is yours in Christ Jesus, 2:6 who, though he was in the form of God, did not count equality with God a thing to be grasped, 2:7 but emptied himself, taking the form of a servant, being born in the likeness of men. *
You interpret this to mean the Second Person of the Trinity changed Himself, changed His mental state. However, consider that if from all eternity, a characteristic of the Second Person was a humility that “did not count equality with God a thing to be grasped” and from all eternity intended to take the form of a servant, THEN THERE WAS NO CHANGE IN THE SECOND PERSON when He took “the form of a servant” - it was all eternally a part of Him. The actual coming into existence of the human body and soul of Jesus occurred in time, experienced change. But that took place in the human nature, not the Divine nature of the Son, the only Person present in the incarnate Jesus.
You may find paragraphs 461–478 informative regarding the Incarnation.
In Catholic teaching, both the Trinity and the Incarnation are considered “mysteries” - that is, revealed truths beyond our human comprehension. We know them only because God has revealed them to us.