I did, but missed the second link. Reviewing it, I still don't see the part that supports your claim that it outlaws letters of marque and reprisal. Privateers are not "militia" nor are they "volunteer corps". They are on their own.
You can't have it both ways. Either they are on their own, or they have government authority to act.
If they are on their own, then there's no need for Marque and Reprisal.