I think one can make sense of PAE by recognizing that the reason people have difficulty articulating a moral account that can ground an argument from evil is that they are trying to ground it on the wrong kind of concept. The fact that you find, over and over, that arguments from evil break down into a moral incoherence despite being onto something that obviously should be taken seriously, is that people assume that because they concern evil that the key concept is the good. They then take a conception of moral goodness and try to macguyver it, rig it, to convey what they are actually trying to convey, and since the concept is not well suited to that, the results are rarely good. I think this is a point at which Hegel and the Absolute Idealists were actually correct: the key issue in arguments from evil, and theodicy in general, is not the good but the sublime. This is the solution to the PAE: people are trying to rig up moral goodness to handle a job for sublimity.
Why would someone do the difficult work of trying to climb a mountain, or going out to sea? Necessity could be a reason, but it's not a very inspiring one. One of the key justifications of doing and enduring difficult things is sublimity -- you climb the difficult mountain, you endure the difficult trial, because, having done it, the success is sublime and makes it worthwhile. The problem people are trying to articulate in arguments from evil is not usually -- outside of some very narrow philosophical contexts -- the bare existence of badness. What they are trying to articulate is that they don't see that there is any complete context in which you could set the trial and difficulty of a world filled with evils that would be sublime enough to make the trial and difficulty worthwhile. It's the worthwhileness in particular that is the source of the problem: how can it be worthwhile to endure a world with such evil in it? That this is the real issue is, I think, especially obvious with arguments from natural evil, but it is also clearly the case with many arguments from moral evil.
There are, of course, a few exceptions; sometimes it's really just revulsion at a very specific evil that is the motivator, and sometimes moral goodness itself does play a genuine role in the argument in a way that is not incoherent. But even these would often be better framed in terms of sublimity, that there is no context sublime enough to turn endurance of this or that kind of evil into a trial or sacrifice that is worthwhile. And of course, we see that this is also really the issue addressed by theodicies -- they attempt to identify something sublime enough. In any case, thinking in terms of sublimity bypasses completely the point that usually makes either arguments from evil or theodicies break down into incoherence.
