the basic problem with an issue like abortion is that you cannot make a compromise without undercutting the central rationale for your position
this is true for both sides
if you believe that life begins at conception, then abortion under all circumstances is taking human life
if you believe that a woman should have absolute control over her body, then any interference on the part of the state is unacceptable
I don't believe that this is necessarily true for both sides. Yes, if you believe that life begins at conception then abortion under all circumstances is taking a human life - this is true. However, I think you've slightly mischaracterized the mainstream pro-choice position. It is not necessarily that a woman should have "absolute control over her own body" whereby "any" interference from the state is unacceptable but rather that the state's interest in the fetus' life and/or protecting the mother's health does not become "compelling" enough to override a woman's right to privacy until certain stages of the pregnancy.
I'm sure that there are a percentage of pro-choicers out there who believe the state should never prohibit a woman from obtaining an abortion under right to choose/privacy/own body concerns, but I don't find this to be the prevailing mainstream view.
The Roe Court broke down the pregnancy roughly into three trimesters (technically first trimester; end of first trimester to fetal viability; fetal viability to birth) and evaluated the competing interests between a woman's right to privacy and the state's interest in the fetus' life in each:
First trimester: an abortion is generally safer than childbirth and the state's interest does not reach that of the woman's right to privacy. There's no compelling reason for the state to pass restrictions on abortion for the mother's health.
Second trimester: state's interest in protecting the mother's health becomes more compelling and therefore the state can regulate abortion to the extent that it is reasonable to protect/preserve the mother's health.
Viability/Third trimester: state's interest in the fetus' life is compelling and therefore the state can ban abortion in furtherance of this compelling state interest. Here, in the Court's opinion, the state's interest reaches a point overriding the mother's right to privacy.
I actually find Roe v. Wade to strike an impressive balance in the abortion arena and that the Court addressed competing legal interests quite well particularly for a decision in 1973. This is the primary reason I'm concerned about overturning Roe - that any future decision by the SCOTUS would be more likely to be entrenched in an ideological polarizing conflict rather than a logical step-by-step analysis of competing legal interests at various stages.