A mother doesn't give up that right to bodily integrity simply by voluntarily sleeping with someone. So it's till a "competing right" if that's the way you want to cast it. And reasonable is giving the rape victim two choices. You can take an abortion pill now, or you can wait until the baby can be "evicted" without harm to your or the baby. With modern incubation technology that is
not nine months as you asserted. Further, decades ago we had the ability to do embryo transplants.
http://www.rfreitas.com/Astro/FetalAdoption.htm
Like you said. Life isn't fair. All you've done is transferred unfairness from mother to child. And at no point is the pregnancy is there a lack of duress for the choice so that really isn't worth factoring into the argument. It's better for the mother to make the choice early in the pregnancy. She doesn't know the child's sex. There is less wear and tare on her own body. At this point there is no nervous system or heartbeat so it's less arguably a "life." In fact most consider the morning after pill not to be an abortion at all as it usually (some argue always) works by preventing the egg from being released. So you're asking a woman who doesn't want to be pregnant to make the only sensible choice possible.
I'm not sure where you are going with the JW analogy. Are you suggesting that you don't ever agree with a mother, even a rape victim, taking an action that kills the fetus? That's the Walter Block argument. (Evictionism). I can go along with that position. I don't think it should be relegated only to victims of rape though. But that doesn't seem to be what you were saying earlier.