Consistency: I don't exactly get what you're aiming for. I have had more than once a “tipped over” salt-out that held a ton of salt crystals between a very soft and mushy soap curd, that went rock hard over a few weeks (like salt bars). I imagine these are easy to crush into a powder (though they'll contain a ton of salt). Other salt-out actions resulted in an agreeable, pliable lump that was easy to shape (somewhere between HP batter and soap dough; easily put into silicone moulds).
I've not nailed down what was the difference, I suspect it is how vigorous one whisks the solution just after adding the salt. Not entirely sure (darn, didn't take notes), but I think the best (smoothest, most HP-like) results were from batches I didn't stir at all, but let the boiling brine do all the work for me (steam bubbles kneading and circulating the semi-fluid soap mud. Let it boil briskly for several minutes, use a spatula only to assure nothing is burning at the bottom; if you have added enough salt, it won't.).
However, I wouldn't classify the outcomes of salting-out between “crumbles” and “curds”; for the former I suspect other mechanisms to play a role (not boiling?). But then, I haven't read through KimW's efforts (yet).
Fatty acid profile: High-lauric and high-oleic/linoleic recipes don't work too well; some palmitic/stearic acid is important, otherwise the cake won't solidify upon cooling, and you can't separate the soap from the brine/glyerol. In winter, I could put the pot outside. Lard-based recipes should pose zero issue here.
There is a layer of dirt/mud/something sticking at the bottom of the soap cake swimming in the pot. This is NOT WORTH dealing with. Scrape it off and discard it. You'll lose a few % soap (but keep in mind, if you hadn't salted-out, you'd maybe lost everything).
Pot size: At least triple the volume of the soap. You'll add quite some water, and you want to have enough headroom for a well-behaved overboil.
Multiple salting-out: Yes, it's fun and impressive how clean one can get a soap that looked like waste initially. However, multiple rounds of salting-out also means multiple risk of over-whisking (bad separation between brine and soap), more time, more salt.
Amount of salt: that's a difficult one. I have had second salting-out rounds where the brine that had been kept back in the solidified soap disc was enough to trigger separation without any additional salt, just by heat + a bit of water. Obviously, it should be no more salt than can dissolve in the water. Which can be tricky to estimate when you haven't tracked the amounts of everything™ (which is impossible anyway). Some salt will inevitably carry over into the final soap, but the average salt-out soap doesn't make the best salt bar.
Superfat: Kill it only if you are unsure about the “state” of the superfat (suspecting elevated DOS danger). Add some NaOH into the first dissolution water and let it react (similar to HP, give it some time). At the very end with the glycerol addition, you then can (should) add your favourite superfat. But in case you're unsure about rancidity, it might be just as fine to toss one or another of the input batches, before ending up with a unsightly end product.
You might consider adding soda ash instead of NaOH to the brine. It'll neutralise free fatty acids (DOS precursor?) without being too aggressive during the process itself, as well as in the finished soap (you don't want to have pockets of NaOH lye in there!). In fact, if it weren't an irritant by itself, sodium carbonate would make even a better salting-out agent than sodium chloride (Hofmeister series).
Finish: Somehow you'll have to turn the cake into whatever shape you want your soap to have. Raw material on the softer side is pliable at room temperature, otherwise the way is open up to (oven or stovetop) rebatch-alike. However, I noticed that at elevated heat, young rebatch soap tends to “sweat out” excess brine from hidden pockets – which doesn't have to be a bad thing, but can be undecorative.
You'll have to replace the lost glycerol. You might now also want to add EO/FO/colourants/botanicals/exfoliants. Citrate/gluconate/EDTA. ROE. Superfat.
Cure time: At least with my trials, salted-out soaps need a substantially longer time than CP or HP to become hard enough to not instantly dissolve in water. One batch was still too soft after two months, another just barely usable. I wish you best luck that yours hardens up to your expectations in a decent time!
I found instructions on the Soapy Stuff website for making soap powder and adding essential oil. I think I should do the extra lye step in the salting out, especially since some of my soaps may have had a bit more oil added with colorants. Now all I need is some free time.
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