From our human point of view, it seems sensible that the overall texture of a mostly-potassium soap should smoothly and gradually shift from water thin to honey-like syrup to smooth gel to firm solid as the percentage of sodium increases in the soap. From the soap's point of view, that is absolutely not something it wants to do.
Sodium soaps really "want" to be organized, so that's why sodium soaps prefer to take a solid form or make a ropy gel depending on water content and fatty acid content. The solidity of a bar soap or the ropy-ness of a sodium-soap gel is the result of those sodium soap molecules trying to organize themselves into some kind of structure. Sodium soaps will finally end their quest to be organized only when the water content gets very high. At that point, a sodium soap will form a watery-thin solution.
Potassium soaps are less particular about being organized into a framework -- they're naturally more disorganized. That is why a potassium soap can range in texture from soft sticky paste to smooth gel/syrup to water-thin liquid, again depending on water content and fatty acid content.
As you dial up the sodium content in a mostly KOH recipe by adding more and more NaOH, you're very likely to see exactly what Susie has seen -- a fairly abrupt shift from mostly disorganized potassium soap behavior to mostly organized sodium soap behavior. I won't say it's impossible, but I do think it's going to be tough to find a precise mixture of Na and K and fatty acids and water content that produces the human ideal of a thick syrup or gel that stays pourable and doesn't get ropy. We're wanting a soap that is carefully balanced between sodium-soap characteristics and potassium-soap characteristics. That will be a challenge, because a soap generally wants to behave one way or the other, not somewhere in between.