"[I]t may still be worth asking why some people are likely to think it's creepy to clone a human being."
As long as conception is out of human control, it's easy to think of yourself as your own person. Once it's under someone else's control, it's harder to think of yourself as your own person.
"A better way to frame the issue might be: what, if any, ethical questions are raised when you produce a human being in any fashion other than random genetic/sexual roulette? Is it in some way essential to our sense of individual uniqueness that nobody had any real control in advance over what our genes would be like?"
Our society's system of rewards and punishments for behavior is based on the idea that we individually create our own lives and make fundamental decisions with a ghostly faculty called "free will." We are rewarded with wealth and prestige for our own virtues, and we are punished by poverty, shame, and incarceration for our own transgressions. While this premise isn't ultimately true, it's the foundation of our social system. As long as genetic endowments are handed around out of our sight and control, it's easy for us to think that our actions are our own, and that we really deserve our good jobs or our prison sentences. But once genetic engineering pulls back the curtain and lets us see the little genetic man pulling the levers, the very basis of our social system is called into question. If I couldn't take pride in my own privilege or feel good about punishing those that are punished, well, what would the world come to?
Not to say that our entire character is determined by our genes. Only about half of it is.
"If you knew that your genetic makeup had been entirely designed in a lab in advance by people who understood exactly how and to what extent each gene would affect your personal characteristics and traits, how, if at all, would that change your sense of selfhood?"
It would change my sense of selfhood in exactly the way that my sense of selfhood was programmed to be changed.
"The only thing that would stick in my craw would be if somebody purposely designed me to be less than fully functioning in some area."
And it would only stick in your craw if your genetic programming allowed you to take exception to your fate. If you were designed as a menial laborer or sex slave who loved being a laborer or slave, it wouldn't stick in your craw.