"If we consider abortion to be morally wrong on the level of murder, then it logically extends that we ought to punish the mother if she was complicit in the abortion process."
Fine. Now show why we should consider it to be "morally wrong" without bringing up superfluous entities such as gods.
"I got to thinking how law enforcement officials could prove beyong a reasonable doubt that an abortion had taken place, and the only conclusion I could come to is that women should be mandated to recieve maybe quarterly examinations of their uterus, under threat of jail if they refuse."
I'm pretty sure that would be a violation of privacy at the least, not to mention a violation of some human right or another.
"Or maybe make pregnant women register and then if they "miscarry" then an exam will be ordered."
Yeah. Let's start making people "register" for all kinds of shit that's nobody's business but their own. I hear that's what all free societies do.
"Women who have been found to have undergone abortion should be held as accomplices to murder, maybe conspirators as well, and then punished according to our preexisting laws on the subject."
We have no laws that would apply. See, murder only applies to actual, full-born, living, breathing human beings.
A clump of cells or a barely formed "baby" that looks like something out of an Aliens movie doesn't count since it's none of those things mentioned above. You can't really "murder" something that can't even survive on its own.
"If I really feel abortion is murder, then it necessarily follows that the people responsible for the murder ought to be punished."
"If" you feel abortion is murder? Who the hell said your opinion counts? Nobody gives a fuck what you "feel" is right or wrong.
You're just not that important, pal.
"Retributive punishment will deter and influence women away from baby-producing activities, and hopefully reduce the amount of abortions."
Yeah, right. Sure it will.
You know what happens when you ban something? That something becomes a black market item. There's no fucking way to regulate damned near anything. A new market will be created the second something is banned/outlawed/ceases to be produced/etc. Then all you end up with are a bunch of people who are unqualified to perform abortions doing it because there's money to be made.
Sounds like you haven't really thought this whole idea of yours through completely.