Thanks for the reply. Regarding Kristan Hawkins, I said in my previous comment that I think most of her arguments are good. I agree that the CMP videos certainly do not end the debate over abortion victim photography. That being said, however, she still seems to deny or at least downplay the significance of the thing that sets the fourth video apart from the first few (the "war-torn" corpse of the little boy, and the reactions of the Planned Parenthood staff). So I stand by my earlier assessment of the article.
I've been following your work for quite a while now, and I know that you don't actually think abortion is like a mathematics problem or a Rubik's cube. I appreciate the honesty in the two articles you linked, and it really says a lot coming from a veteran pro-life activist. This quote pretty much describes exactly how I felt when I saw the fourth video:
When I get upset, I have an immediate impulse to take all of my opinions with a grain of salt because I feel like I’m not in control. I’ll tell Josh “my compass is broken right now,” meaning I don’t trust my intuition, just like I wouldn’t trust a compass that I thought might not be pointing north.
Yesterday I emotionally broke down, but for those few minutes my compass was pointing true north. I’m less emotional now, and I trust my compass less.
At the end of the article about the OMSI exhibit, though, you write that some days you don't feel as sadly about abortion as you ought to and that you are sometimes disconnected about how awful it is. This really sounds a lot like what I said above: unintentionally (and probably subconsciously), there is a tendency to act like the abortion issue is an abstract philosophical exercise. The blind spot is still there, even though you’re aware of it and are trying to avoid it.
Regarding philosophical arguments, I think they’re important to a certain extent. However, they have severe limitations. As your friend Trent Horn (who is even more philosophically-minded than you are) puts it, philosophy makes people so smart that they turn into idiots. Let’s suppose that critics of the pro-life position come up with a very intelligent argument for legalized abortion that we’re unable to counter (perhaps after years or even decades of trying). Question: should we become pro-choice if that happens? I believe there are very good reasons to say that the answer is “no”. This sounds strange, but let’s look at an analogy. Zeno of Elea was a philosopher in ancient Greece who proposed that motion is impossible because in order to walk across a room, for example, you would need to first walk halfway there. Afterward, you would need to walk half the remaining distance, then half the remaining distance, and so on. Because this would add up to an infinite number of tasks, and it’s impossible to complete an infinite number of tasks, it’s impossible to walk across the room.
The first person to challenge this argument was Diogenes of Sinope, who demonstrated that the conclusion is false simply by getting out of his seat and walking across the room. Philosophers don’t like his “rebuttal”, of course, because he didn’t actually refute any of Zeno’s premises or show why his logic is wrong. The most common strategy for countering it requires a knowledge of infinite geometric series, limits, and (if we want to be really precise) delta-epsilon proofs – the latter of which wasn’t developed until the 19th Century. Even today, there are still some philosophers that reject this argument (and other proposed solutions to Zeno’s paradoxes).
For thousands of years, Zeno and his supporters arguably had the better argument. Some would say they still haven’t been adequately countered. Yet no serious person actually believes that motion is impossible. Walking across the room is enough to show that the conclusion is self-evidently false, and that the whole analysis is nothing more than an amusing intellectual exercise. The CMP video is to pro-choice arguments what walking across the room is to Zeno’s paradoxes – it doesn’t directly refute them, but it does demonstrate that abortion is a barbaric practice that no just society can tolerate.

there is a danger when spending a lot of time speaking philosophically about abortion to unintentionally sound like we think abortion is merely a Rubik's Cube to be solved. It's not. . . . There was literally weeping in our office watching the CMP videos. After making the Rubik's Cube comment though, we add this: "But if we are going to respond to the most intelligent arguments that the pro-choice side has to offer, we're going to need to respond with more than emotional arguments . . ."
If I understand correctly, your distinction here is between only two factors involved in decision-making for oneself and in the persuasion of others. (The persuasion of others means influencing the decision-making of others.) The two are discursive argument / logic / rationality, and emotion.
And one point you make is that you don't want to sound like you have suppressed your emotions (or presumably to actually suppress your emotions). You call the possibility of doing that a danger.
But there is another factor, which you have sometimes referred to, in decision-making on moral issues (or influencing decision-making), and that is moral intuition.
(Distinguishing between emotion and moral intuition: Suppose that tomorrow morning I read in the news that half a million people in Sub-Saharan Africa are expected to die of starvation within a month. And suppose that on that same morning I drop my cell phone and it breaks. I may be more upset about the cell phone than about the starvation. That upsetness is an example of emotion. But if you tell me, "Your cell phone can be saved or the half million people can be saved, you have to decide," an inner voice will tell me that the half million people should be saved, and I will follow that voice. That voice is my moral intuition about that particular situation. And I think that in many people, that voice will often override their emotions.)
And, along with there being another factor, I think there is another danger: believing that we can prove a moral point through discursive argument / logic / rationality* without reliance on a moral intuition that is not at all rational -- that comes out of our unconscious in some way we cannot understand.

• Or even advancing our arguments as if we could prove a moral point through discursive argument / logic / rationality, while perhaps acknowledging, as a formality, that we cannot.
  [Edit: In other words, is the abortion issue or any moral issue ultimately a Rubik's cube at all, ultimately tractable to discursive argument / logic / rationality at all? (Not to deny that those are very important tools.)]
  I think the danger is that our discussions will be no more productive than they normally tend to be. I think they will become more productive if we can become more aware of the limits of discursive argument / logic / rationality, and what causes those limits to exist.
  I have tried to think about the ways our discussions will be more productive http://www.noterminationwithoutrepresentation.org/moral-intuition-logic-and-the-abortion-debate/, in a short section called The Practical Implications.

Thanks!