Take a look at Al Roth's blog:
http://marketdesigner.blogspot.com/
He is an economist who designs transactions for repugnant exchanges.

As the death toll from the organ shortage mounts, public opinion will eventually support paying for human organs. Changes in public policy will then follow.
In the mean time, there is an already-legal way to put a big dent in the organ shortage -- allocate donated organs first to people who have agreed to donate their own organs when they die. UNOS, which manages the national organ allocation system, has the power to make this simple policy change. No legislative action is required.
Americans who want to donate their organs to other registered organ donors don't have to wait for UNOS to act. They can join LifeSharers, a non-profit network of organ donors who agree to offer their organs first to other organ donors when they die. Membership is free at www.lifesharers.org or by calling 1-888-ORGAN88. There is no age limit, parents can enroll their minor children, and no one is excluded due to any pre-existing medical condition.
Giving organs first to organ donors will convince more people to register as organ donors. It will also make the organ allocation system fairer. Non-donors should go to the back of the waiting list as long as there is a shortage of organs.
David J. Undis
Executive Director
LifeSharers
www.lifesharers.org

There needs to be some way to compensate donors for their time, risk, and kindness. My brother recently received a kidney from a co-worker. It would have been nice to pay for some of the donor's lost work hours, childcare so his wife could spend time with him, maybe a hotel nearby so she didn't have to travel so far, dinner for her. But no gifts at all are allowed.
Cadaver donors should have their funeral paid for, up to a set amount. Living donors should have all expenses related to the donation paid for, up to a set amount. This provides for their family to be able to support them; recovery time (giving a kidney HURTS, btw); travel expenses; childcare...
As it is, the donor had to use his own vacation/sick time to donate, and while the actual medical costs were paid for out of my brother's insurance, all the surrounding costs were his. And that isn't fair.
I think expenses up to, let's say, $10,000 should be allowed, or funeral costs up to the same. It isn't payment for the organ, it's an allowance to absorb the costs of donating...

One of Professor Satz's central arguments is that legalizing the sale of body parts would impose a cost on people who do NOT want to sell their body parts. I take it this is just an opportunity cost (if I sold my kidney, I'd make some money, so when I don't sell my kidney, I have that much less money).
But creating an economic opportunity doesn't result in my actually losing anything at all. It is my choice not to sell my kidney either legally or illegally, and so even while organ sales are illegal, I have less money than I would if I sold my kidney. Regardless of the legality of organ sales, I don't actually lose anything I have when I encounter an opportunity cost.
I'm not at all confident that organ sales should be legal, but I don't think this opportunity cost argument is a good reason to keep organ sales illegal. Then again, I'm not an economist.

Although I do agree with your post, I have my own reservations.

To my thinking, the social morality (and the legality) of organ selling is and should be intrinsically tied to the propensity and severity of the fraud and exploitation that it will entail.
A certain amount of fraud or exploitation is inherent in the market, as anyone whose ever bought a packet of sea monkeys, or taken a telemarketing job can testify. This is why we have wage and truth-in-advertising laws.
But in most cases, the consequences are relatively minor. If you take a job that sucks, you can quit. If you buy a bunch of brine shrimp imagining that they would form a fun-loving, utopian civilization before your eyes, you're only out a couple of bucks, which you can right off to experience. Not so with an organ transplant.
If you sell your kidney and later realize that shortening your life by ten years wasn't worth the used camarro you bought with the proceeds, it's too late. There's nothing you can do (short of buying someone else's kidney, perhaps) that will mitigate the damage that's already done.
If you sell a kidney under duress or in following self-serving medical advice from someone looking to buy your kidney, the organ is gone, your lifespan is considerably shortened and there's nothing you can do about it. You can't simply chalk it up to experience and you can't quit being a former kidney donor. You can sue the person or organization that defrauded you, but even if you win, that won't bring your kidney back. The simple truth of the matter is that when it comes to organ-selling, there's no way to adequately address the consequences of someone being swindled out of a kidney. Any legal protection that matters must happen on the front end of that transaction.
If you allow people to monetize their life-saving organs, there's a very large incentive for people to defraud and exploit them. And the consequences of being victimized in this manner are so dire, that given these facts I think a society has the moral obligation and legal right to step in and regulate or even ban organ selling in a way it doesn't with other, more benign transactions.

It is of some interest, I think, to consider that the entire enterprise of organ donation and transplantation was the stuff of science fiction, not so many decades ago. Be that as it may, there are numerous arguments, for and against this miracle of modern medical science.
Certain fundamentalists may argue against it on religious and/or moralistic grounds. Science, on the other hand, is more pragmatic and generally unfettered by religious dogmas and moral high ground: we have done it; we can do it; it extends lives (for some or many); and, some folks (or their medical insurers) can or will pay the price.
Black marketeering is only one of many ways in which humanity engages in corruptive behavior. We should not be so shocked, because it is also a part of world economy.
An ex-coworker "gave up a kidney" for his brother, about fifteen or twenty years ago. He died before I retired. I think the brother (younger and diabetic) died also. We do the best we can with what we have. Sometimes.

Donating organs is very honorable. Buying them means some people are not on the same level playing field. Do the wealthy deserve them more? That is the question you must ask yourself.