No, the problem is that they are "should" questions, and thus experiments can't answer them at all. Now, if you assume a moral framework in which a certain combination of consciousness or intellectual capacity on the part of the mother makes her rights paramount (or one which does so for the child, or one which does some calculus on the relative levels of those traits between the mother and the child to determine which is paramount) then you can reduce this to a fact question that is conceivably resolvable by experiment (and, thus, leave only the problem that you mention), but I would assert that there is no such consensus moral framework, so you've actually identified the easy problem with resolving the conflict, while ignoring the fundamental and intractable one.

This is a fruitful example: the vast majority of those opposed to abortion will concede that a zygote has no conciousness or intellectual capacity, yet most of them will nonetheless insist on the zygote's personhood and right to life.

Exactly.