After much consideration...
aka laziness, I think I'm ready to respond.
Regarding our personhood in relation to God, maybe an analogy will help. I create a clay sculpture in my image. Some are larger, some are smaller. I consider all of them to be in my image. I also create a wooden toy dog. This is not in my image. So it is with God. He created us "in His image and likeness". Now, I don't believe that that means God looks like us or vice versa. I believe that it means that we have certain qualities that God has. Call it a divine spark or the breath of life. It is this thing that differentiates us from the animals. It is perhaps the Ultimate Potential. It's what makes us creative beings. It's what drives us to philosophize, write poetry, examine the universe, etc. These things are unique (afaik) to humans. We all realize this potential to various degrees based on our own stage of development. Some never get the chance, but that doesn't make them less human. A dog or a chair or a rock never has that potential. Does that make sense?
So I think I'm still on sold ground for saying that in the SLE there are no meaningful degrees of personhood. All human life is sacred, even that of a murderer on death row.
You go on to say:
This leads me to another train of thought. I’m confident that you would agree that one who is senile is still created in the image and likeness of God (a person), yet we don’t grant them the rights of a mentally capable adult; the power of attorney, for instance. Nor do we grant equal rights to children based on their potential to become adults. If not degrees of personhood, what criteria are you using to justify the differing moral rights?
So given what I said above, both the senile and the young have a right to live. "Life, liberty, and the pursuit of happiness" are among the inalienable rights that the DoI says that we have. I suppose we have branched out from the right to simply exist as a person to other rights, which makes this more complex. For these other rights then it becomes not about someone's personhood, but about qualities that a person has, maturity, intelligence, etc. This gets to how that potential is realized. In my opinion this doesn't make someone more or less deserving of life itself. It only limits how they may express that life, or live it out. The right to power of attorney or to go buy a beer or those sorts of things isn’t inalienable in our society.
Given that, when you say "An adult woman, by way of contrast, has both of these interest plus many more, such as an interest in avoiding the pain, expense, inconvenience, emotional hardships, and health risks of childbirth. Her multitude of interests trumps those of the fetus." I rebut that this woman isn't guaranteed by anything I'm aware of to avoid certain expenses, inconveniences, hardships, etc. Naturally she may want to, but what moral law do you use to ascribe those rights to her? The above "inalienable rights" or only guaranteed insofar as we don't abridge the rights of others. And now this is getting out of moral and into legal areas I think.
Finally given your final paragraph:
Using this version of the QLE, it is easy to see why a woman’s prerogative does not extend to after the birth of the child, at least not in our modern society. The main suffering a postpartum mother would experience result from the on-going care of the infant. Infanticide is not justifiable because our society provides an alternative that does not infringe upon the infant’s interest in survival and does not require the mother to assume additional suffering; adoption or foster care. There is no question that these options are morally superior to infanticide since they reduce the suffering experienced by the infant without significantly increasing suffering for any other person. For this reason, post-birth is the rational point to grant a human a moral right to life.
would you say that given our current level of technology and ability to keep a child alive starting some time in the late second trimester that performing a C-section and letting the child have a shot to live would be morally superior to having an abortion since it actually has the same affect of removing the baby from the mother's womb and keeps the baby from losing that one thing it has? That is assuming that the mother wouldn't be liable for expenses incurred.