Primarily, prohibition made a dent in the amount of drinking. Not a significant dent. Just in Chicago Al Capone ran 10,000 speakeasies. In addition, the Volstead Act (sect 29) allowed for the making of up to 200 gallons of home made alcoholic fruit drinks (not including beer), and it was common practice to sell grapes or other fruits specifically for use in creating alcohol at home. So I would say, statistically, it is likely a majority of the people who wanted a drink had a drink through either some legal loophole or illegal scheme.
That being said, on an issue such as abortion, it seems to me to be less likely that laws would affect a person's choice. It is much easier to not have a drink (for most people) than it is to deal with pregnancy for nine months, followed by a painful birthing process, followed by raising a child (as while adoption is an option, a large majority of people who have a child keep it). So I think that saying abortion laws would reduce abortions by 70% is a gross overstatement. That being said, there's no way I can prove that statement, it is just what I have concluded by looking at the data available to me.
I think that the phrase "Many religions and ethical codes (including my own) do exactly that." sums up perfectly the problem with anti-choice argument, and that is it assumes that a person holds a specific religion or moral code, or that a specific religion/moral code is correct. Morality is seen differently from every person in every situation, and morality is seen differently by an individual in different circumstances. You may be surprised to know that your perception of morality shifts more than you might think, as "personality traits", including personal belief, only run about +.3 to +.4 correlation with a persons response to a situation. Which means that the rest of the time, despite a person's beliefs on ethics, the outcome is largely decided based on factors outside his or her control, such as the situation (which also runs about a +.3 to .+4 correlation between individuals, for example).
This goes to show, I think, that making any laws about morality which force a person to do a specific thing should be considered gravely, and from as much of an unbiased view as possible.
And no, slavery should have been outlawed as early as possible because the slaves were, in fact, people. We now consider people to have natural rights (I think all sentient beings have natural rights, and this is an opinion most of the world shares). People did not consider slaves persons, which is why they were misinformed about the morality of the situation.
I'll cut off the argument of "unborn babies are persons and thus should not be able to be aborted, just as slaves are persons and should not be put into slavery" now. This would be a valid argument if an embryo or fetus before the third trimester had an ability to feel pain, like a person of African descent does. As it is now, our leading scientists state that it is hard to determine exactly when a fetus has the capacity to feel pain, but it is extraordinarily unlikely that this point is reached until AT LEAST the third trimester.
And an embryo is no different than a single egg or a single sperm in the matter of "sentiency"--the only difference is it is growing. But it is most definitely not a sentient being--if it is, then all simple organisms could be considered sentient beings, at which point the it would become immoral to trample on the rights of the common cold germ (and our thoughts about natural rights would have to be completely re-examined).
I think my take on the morality or immorality of abortion is a non-issue when it comes to making a blanket law about it. There are some rules that all people of all creeds can live by, but as for the rest--we have too many rules trampling a person's ability to be free as it is. Do we really need more, especially on such a controversial issue as this?
(that being said, I know nothing I say could convince you against your point, and likely the same is in reverse. I make these statements more to demonstrate why I believe what I believe, rather than try and convince you to change what you believe)