Thanks so much for posting these recipes. Absolutely fascinating!
There's a lot to ponder here. A few quick things I notice right off the bat:
The first recipe has the option of not using slop or backset of any kind, and seems to me very much like it might be derived from a beer (i.e. lager, ale, etc.) recipe. It seems like it would taste "sweet" during the mashing.
What is slop??? My guess is this: slop is what you feed the pigs. I'll have to look around for a recipe for pig slop... it's possible that the remains of a distillation run might not be nutritionally sufficient, so there might be added grains... thus the slop might be capable of supporting living yeast. Or maybe no added grains, but the original fermentation didn't use all the starches/sugars, and so as the slop sits around for a few days it continues to ferment. According the the second recipe, slop can be "very hot". Hmmm. Harder and harder to figure.
The use of wheat OR rye as an adjuct grain: how curious! This leads me to all kinds of elaborate theories.
The second recipe: the mash would certainly taste sour! Why do you wait so long with the corn meal? I guess you're letting the starches dissolve. In this recipe: rye is the only option, not wheat. Whew! At least that lets me keep the Tim Dellinger Theory of Rye as an Adjuct Grain intact.
My feeling is that the second recipe is very much a sourdough-style recipe, with yeast and bacteria fighting it out and reaching equilibrium and doing all kinds of interesting things. The first recipe you pray that bacteria never take hold; in the second you acknowledge and leverage the presence of the bacteria.
It's possible that today's sour mash process bears more resemblance to the first recipe than the second.