The IEEE equations (D.8) are empirically derived from test data. This means, unfortunately, that they have little (known) physical basis. The equations in section D.8.6, D.8.7 were further derived after additional testing, usually on the behest of some manufacturer, so that they could say their products are better because they are current limiting.
Current limiting does work, and that is part of the reason why these equations are different. They assume that the device will operate, usually within a quarter of a cycle, and that the current will never reach the peak value, which is what you have input into the equation. So, to put it simply, there is less current, and less time, so less arc flash.
I don't know if you could reconcile the two sets of equations. They are based on different assumptions, but even more, they are based on different test data. Hopefully, the next round of testing through the NFPA/IEEE partnership will yield a physics based set of equations, and will put many of the current problems to rest.