Potassium carbonate vs. Potassium hydroxide in Wood Ash
You can never get $\ce{KOH}$ directly out of wood ash. One can recall that potash $\ce{=K2CO3}$ is indeed pot-ash! So you are right that historically calcium hydroxide was needed to obtained $\ce{KOH}$ out of potash. The rest of the stories are all false. $\ce{KOH}$ is unstable in air with respect to carbonate formation. It is hygroscopic as well. Wood ash remains bone dry forever. I don't think there is even a trace of potassium hydroxide in wood ash.

Until and unless you don't have a furnace, which can generate temperatures above 1300&cir; Celsius chances of getting $\ce{KOH}$ in useful amounts are almost negligible.

Secondly, a soap made with tons of calcium salts will be nothing but literally scum (=insoluble calcium soaps). Calcium should not be a part of soap.

Here is a nice abstract on the composition of wood ash as a function of temperature. [1]


  The elemental and molecular composition of mineral matter in five wood types and two barks was investigated as a function of temperature using thermal gravimetric analysis, differential thermal analysis, inductively coupled plasma emission spectroscopy, and X-ray diffraction. Low temperature ash was prepared at 500°C, and samples were heated in a tube furnace at temperature increments to 1400°C. The dissociation of carbonates and the volatilization of potassium, sulfur, and trace amounts of copper and boron were investigated as a function of temperature. Overall mass loss of the mineral ash ranged from 23–48% depending on wood type. The mass of K, S, B, Na, and Cu decreased, whereas Mg, P, Mn, Al, Fe, and Si did not change with temperature relative to Ca which was assumed to be constant. Sintering of the ash occurred, but fusion of the ash did not occur. In the 600°C ash CaCO3 and K2Ca(CO3)2 were identified, whereas in 1300°C ash CaO and MgO were the main compounds. The implications for ash deposition in furnaces is discussed.


References:


Misra, M. K.; Ragland, K. W.; Baker, A. J. Wood ash composition as a function of furnace temperature. Biomass Bioenergy 1993, 4 (2), 103–116 DOI: 10.1016/0961-9534(93)90032-Y.