No dirt in my shaving soap please!
Aside from reading the thread Songwind started, try this: 52% Stearic, 48% Coconut, KOH only, 5% superfat. HP only (or do take a video with sound so we can hear you swearing!). Let someone experienced with shaving soaps try it and start from there. That will give you the quickest/easiest example of what can be a good shaving soap and let you see all of the properties that are so different from a cleansing soap.
Starting with that I actually found I could go with less foam so I started subbing out the coconut for others, but that basic formula is so much better than what you can buy in a store and so simple to whip up, it's ridiculous.
No it won't make a puck, we call it a "croap", a cross between a cream and a soap. Typically one would load a wet brush for 20-30 seconds and then lather in a bowl.
Also, and please excuse me if it sounds like a beginner lecturing experienced soapers but this is an observation: The Songwind thread is an EXCELLENT example of where folks go wrong by overthinking it. I know there's folks on here who may make a business of creating and selling fantastic soaps. If you are that person then I'm pleased to have folks like you around to learn from. If I may be so bold though: don't over-think this. Don't add clay, oatmeal, honey, seaweed, or oil of unicorn. Understand this is not soap that is supposed to be in a pretty shape, a pretty color, or have magical properties. It's a vital part of a man's grooming regimen and the first thing we want is a shaving soap that lets us shave. Get that down and then "enhance" as needed.
Being a HP soap it really lends itself well to a small/quick batch. I can make a 100g batch and shave with it that day. Attached is the recipe for the very first soap I made inspired by the same information that lead to Sonwind's post. If that was the only soap ever available for the rest of my life, I'd be okay.
ETA: I only saw the first page when I wrote this - I failed to see that it's 5 pages long. I still earnestly believe every bit of what I wrote however. IrishLass, if my dearest made me soap I would indeed count myself a lucky man. She does not (I'll still keep her!) so this is what I learned in a few years of really learning about (commercial) shaving soaps. I agree, no need to send yourself off the deep end by trying to remove clay because some moron (me) said no dirt. Your recipe works and that's awesome. My comments were more toward someone just taking on a shaving soap.
View attachment MdeC Clone.pdf