Adam,
I just had a thought. Instead of analyzing par 3 holes in the traditional fashion, could you look at them in light of the Broadie/Fawcette type strategy of modern day?
We have all seen the tee shot strategy, usually knowing that the total dispersion pattern is about 20% of length, i.e. 60 yards on a 300 yard tee shot, so aim at least 30 yards away from trouble, but I'm not sure how they attack the similar strategic thinking on par 3 holes.
My first thought might be that the Eden Hole isn't a terrible concept, especially if there is a deep sand hazard or water vs easier hazards on the other side. Of course, many greens feature this, but again, the chance to test that statistics strategy from distance controlled tees and the perfect lie might make it even better on par 3 holes?
Also, it seems like at least one par 3, focused on distance control, i.e., shallow greens might be considered in a set of 4, and as mentioned, the 45 degree green, a la Augusta 12 could be an oft used type of green.