My position isn't that they are mutually exclusive - rather they should both be taken into account (with rights being dominant in the majority of cases, at least as it pertains to law).
Well I guess I have to count this as progress don't I? If you're seeing rights being "dominant", maybe I've at least moved the needle a little.
I just see several cases of suffering (or immorality) that, because of focussing only on rights aren't (or wouldn't be) addressed like:
1) Foetal pain during an abortion
2) Experimentation on humans before a set limit
3) Desecration of the dead
4) Pornographic images/videos of virtual, or doctored underage children
Most people treat moral questions like a bit of a gut check. And when their gut doesn't line up with their head, they go with their gut. That's not a bad thing, that gut (or ingrained instinct or deeply learned belief) is probably there for a good reason. But the gut is not infallible. People go with their gut when they say that drag shows are evil. People go with their gut with xenophobia too. I think it's important to learn to be skeptical of these kinds of responses. So let's look at your list.
1) Pain
First of all, pain is not something that is automatically bad. Your example suggests that the problem is actually causing pain to something that can be considered innocent - which would be a rights violation if that thing had rights. But I think it's important to remember that morally you can't regulate pain. It's something that we experience when we break up or get broken up with. Pain it's something you experience at the doctor's office or if you assault someone and get pepper sprayed.
Pain is almost impossible to define, and you can cast is broadly enough that you could decide that ants, trees, and computer programs feel it. Pain being hard to define, thresholds of pain are even harder.
If something doesn't have rights, we ultimately can cause it pain. Dogs don't have rights, generally, and they experience some pain when they are euthanized. Cows don't have rights, and they can experience some pain at the slaughterhouse or when branded. Death row criminals don't have rights, and they can experience some pain when they are euthanized as well. It may not be a wise idea to systemically cause unnecessary pain, and it may be a good idea to institutionalize practices that attempt to mitigate pain, like anesthetizing dogs, cows, or those to be executed. But this is fundamentally less of a moral question than you might initially think, because it is so hard to define, and because thresholds are so hard to define.
That's regarding pain introduced to a fetus, but it doesn't even consider that the pain you're talking about is one that someone is exercising over a part of their own body during an abortion. It's not even the case of cows, where they are separate entities without rights, it's a case where this is literally part of YOUR body that you control. It's like if the cow could kill you by being alive and you STILL were not allowed to inflict any pain to it to save your own life. That's the insanity of "fetal pain during abortion".
2) Let's say we're talking about experimenting on an 8 celled human embryo. Where is your moral question? This is a moral misfiring. You're mentally attached to the DNA for some reason, and scientific experimentation then gets an automatic no from you, despite the fact that an 8-cell embryo is absolutely not a moral entity. An adult ant has 20 million cells.
3) What exactly are you concerned about with desecration of the dead? When you die, your body is reduced to a pile of tissue, bones, and blood. There is no moral entity there to protect. A lot of people donate their bodies to science, to be practiced on for dissection, to be studied, or for organ donation. Generally speaking, I can't see a reason to get worked up about some spent tissue. But as I mentioned, generally a dead body will belong to someone, it will be the property of that person. And so if you'r worried about how it will be treated because of the surviving people, it will be in their care directly.
4) You've barely discussed this one, so perhaps we should examine this further. I was thinking the other day that we may need something like a trademark for faces. This is not a moral prescription, just like trademarks are not a moral issue, but rather a regulatory exercise, just like trademark, to prevent confusion. Right now, there is a major strike in the entertainment industry, and one of the sticking points is ownership over an actor's likeness. I'm not sure that it should be limited to actors.
When someone draws a sexy fox engaged in adult behavior, how old is the fox? An adult fox is about 1 year old, roughly speaking. Is this a depiction of a 1 year old engaged in adult behavior? What if the person draws what looks like a 10 year old human engaged in that behavior, but the being is actually an alien that matures to this size as a adult? When it comes to fantasy artwork, it's very difficult to determine exactly what is and is not pedophillic pornography. And honestly, I think it's best that we not make the attempt. There is no evidence to suggest that it results in harm for anyone, and there are arguments that it could prevent harm.