Your post reminded me that I need to give an update on my Songwind shave soap adventure.
I made almost the same recipe as my first batch -- 52% stearic, 48% coconut oil, 5% superfat, and distilled water for the water phase. The difference was I didn't use all KOH -- I used 80% KOH and 20% NaOH for the lye.
I saponified just the coconut oil with all of the lye in a double boiler at 180 deg F. I kept cooking and stirring (a bit with a stick blender, a lot by hand) until the batter came to a heavy pudding trace. That took 15 minutes or a bit more. After I got to that point, I added the melted stearic in several stages and stirred by hand. When the stearic was all mixed in, the soap had a "waxy mashed potatoes" consistency. I cooked it in the double boiler for about 15 minutes and checked for zap (nope). I added glycerin (15% of the oil weight), let the soap cool below 120 deg F, added EOs (same blend as before), and finished it up as I have described in a previous post.
Next batch, I want to check (gingerly) for zap right after stirring in the stearic. I suspect it will be fine (but I won't assume that!). I still think my 2 step method of making this soap works pretty nice and will continue to use it.
The 20% NaOH makes the soap somewhat less sticky out of the soap pot. It is also slightly firmer than the 100% KOH version so it was a bit easier to hand shape the soap into pucks. But it is still a soft shaving soap, not a hard bar, so no amazing differences there.
Since I use this soap for shaving armpits and legs when I shower, I keep the soap on a dry shelf in the shower (well, as dry as a shelf in a shower can be). The soap in that environment seems to stay a bit less sticky than the all-KOH version, but no huge differences there either. Neither goes "melty" or super gooey in the damp, but they're never sitting in a puddle of water either. I will keep an eye on this aspect of the soap as it continues to cure and dry.
As far as lather goes, an NaOH-KOH soap is slightly less soluble than an all-KOH version, but at just 20% NaOH, it's a fine shade of difference IMO. As the NaOH percentage goes even higher, I would expect the soap to lather more slowly, requiring a real shaving brush and someone who knows how to use it, rather than a rank amateur like me.
Will I continue to increase the NaOH percentage in this recipe to make a harder shaving soap? I'm leaning toward probably not. I like the amazing lather of Songwind's recipe and I think adding more NaOH will only detract from that. Better to develop a hard shaving bar with other ingredients, as Mark The Box Guy has recommended.