To be cold-blooded about this, that means that if, using your pay scale, you manage to kill Bin Laden, you could kill 99 innocent people who were legitimately in the way, and still make $1M before expenses. This seems like a reasonable, but not extreme, incentive to get a clean kill. If you just go around killing people in the hopes that one of them is Bin Laden (say with area weapons), but no attempt to avoid killing innocents, then that would be reckless and malicious, and you could be charged in the US.
Respectfully, NO. I am just an imaginative civilian with a little Constitutional knowledge, but it seems to this civvie that the last thing you want to do is diminish the efficiency of these operations by hamstringing your contractors. If the contractor is 90% certain that he has a specified Target in his sight, you want him to take the shot if he believes it to be a clean kill... not be so worried about being in the hock for a million bucks over that last 10% uncertainty that he practically has to walk up and ask the target for his photo ID and birth certificate.
For this to be done right, you have to trust Market Forces combined with your contractor's best military instincts to do the job. Think about it -- These guys will not be looking to kill civilians for which they get paid nothing (and after all, Letters of Marque and Reprisal do not protect them against getting caught and tried by a hostile court), and they will be looking to hit the right Target, and get Paid. Killing civilians will only draw attention to them in a hostile environment -- it puts not only their payola at risk, but their lives, as it calls unfriendly notice to their operation. That's a pretty strong disincentive if you ask me.
This is not going to be perfect. Nothing in the real world is. But the natural disincentives operating here -- a military man's aversion to unnecessarily killing civilians if he doesn't have to, a mercenary's desire to hit targets for which he gets paid, not targets for which he doesn't get paid, and an in-country operator's desire not to draw undue attention to himself in hostile territory -- these disincentives are going to be enough to keep these contracts focused, as well as can possibly be expected without trying to micro-manage their operation.
IMHO, this is the deal -- You let them choose their target or targets; You provide them the armaments, gear, and supplies they request (if any); provide them with the best US Intel available on the suspected training-camps/safe-houses etc, in the region in question (additional intel purchases up to the contractor); provide them with whatever forged papers and local currency they require; take them as far as Peshawar or Dushanbe or Tel Aviv or Kuwait city or Lake Van, tell them that upon successful completion they can deliver their kills/captures for confirmation and payment at whatever US embassy they can get to, and turn them loose to do their jobs.
That is how a Letter of Marque and Reprisal is supposed to work. Simple, direct, and uncomplicated.
At least, that's what seems to me. I'll defer to any of the ex-military for comment.