If you don’t already have Chris Blattman in your reading feeds, might i suggest the add? So, can we replace ln(x) with log(yi+(yi2+1)1/2)? Frances Woolley says so. i’m not an economist, so the “auto-reject” from AER isn’t an outcome i’m all that concerned about (see CB’s post here). That said, i do find the solution to computing a log-transformation on variables with high likelihood of zero-values an intriguing one. Perhaps, i should have borrowed CB’s preface of “If you know what ln(1+income) is, and why it’s a headache, you should read this post.”
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Permutations 
Sounds like a decent approach to me, thanks for the links. There is another issue which is sorta related. Take income, one of the most common variables social scientists want to make closer to gaussian through a transformation. In any given year, a fair number of people have no income because they are not employed. The difference between someone not working and someone working for $40,000 /yr is not the same as the difference between someone making $40,000/yr and someone making $80,000/yr.
There are ways to try to make our models reflect this, but its hard, and even you’ve tried to be really thoughtful in constructing it, you can always come up with something else your model isn’t handling very well. But hey, let’s take these little improvements and slowly but surely social science gets a bit better, in at least one limited way, right?