It seems like you don't want to change human physiology much so the easiest things to do would be to increase the efficiency of the bodies. As you said we only absorb 6% of the oxygen we breathe in, so let's find the bottlenecks.
Potential bottlenecks are:
* Airways - The amount of air we can breathe in.
* Blood - The amount of air our blood can absorb.
* Lungs - The amount of air our lungs can put into our blood.
* Body - The amount of air our bodies need to function.
Improve Airways
While the first is the least likely, it's obvious that we breathe faster or deeper when we're in a state where we need more air. A solution would be faster or bigger airways (we also tend to use our mouth for breathing instead of our tiny nostrils). Another issue we face is that we can not breathe in and out at the same time reducing the potential efficiency by 50%. Others here have identified this and claimed that it would work if you had an entry and exit hole, but keep in mind that air needs to flow in and out continuously as well. That would only work with a 2 chambered valve system similar to a heart.
Improve Blood
All of this is meaningless if our blood can not absorb enough oxygen. Since extreme divers hyperventilate before a dive to fill their blood with more oxygen, it seems like this is not the case - on the other hand, athletes try this angle when doping. Some of the things they do that increase the amount of oxygen that can be carried by our blood are to increase the number of red blood cells. I assume some other elements might be more efficient in carrying oxygen. 279
This can also change the color of blood, Crustaceans, for example, have copper based blue blood rather than iron based red blood.
Improve Lungs
As I said, divers hyperventilate to increase the oxygen in their blood. This implies that the bottleneck is the lung. While you suggest that the size of the lung has to increase, this is actually not the case. What's more important is to increase the surface area of the lung. Their lungs could be built like window blinds, like a CPU cooler/heat sink with fins, or similar to fishes gills, which are made for breathing in low oxygen environments. The last two options would work best with flowing air, similar to first suggestions. Since your humans are double hearted and their blood would flow faster, chances are this will become an even higher bottleneck than it already is.
Improve Bodies
Our bodies can become more efficient and require less air to perform the same way. If you've ever tried to get in shape, you might have noticed that at first, you'll be out of breath after a short run. However, once you've trained for a while, you can run for a while until you finally run out of breath. Your double hearted humans could have a better physique anyway and thus not be out of breath as fast. 279