Glad to see these machines getting the attention they deserve. Did you get the dryer also, this was a pair that Tom and I recued and stored for years so I am really glad to see you rebuilding them.

I am quite sure that the WnW cycle does include a cold water suspension cool down before the first complete drain and cold rinse followed by the slow 4 minute spins.

Somewhere around 1961 to 1963, Sears did away with the hi to lo agitation speed change in the wash phase of the W'n'W cycle.  At that time, the wash phase remained normal speed through out agitation as did the rinse phase also stay on normal agitation.  they may have done this to differentiate themselves from Whirlpool which continued that original speed shift sequence well into the early 1970s (I think) when WP decided to split the Knits and Perm Perss cyckles into two differeent cycles.  PP had all normal agitation I do beliveve with two cool down drain and fill phases and the Knits had all gentle agitation as well as only 1 drain and fill cooldown phase.  Knits wash time max was 8 minutes.  The delicate cycle was maxed at 6 minutes and had no cooldown phase on WP. No, Sears may have done some "experimenting", but I do not think they started simultaneously agitating and filling during the cooldown phase fill until maybe 1964.  I know friend's 1965 Model 70 agitated during the cooldown fills on low speed just like our 1970 Kenmore 800 did.

thats a nice looking machine, I am pining for my '55! The things we throw away ---OUCH!

The early WnW cool down was two minutes of draining time, timed by the timer as it entered the cool down phase of the cycle at the end of wash agitation.

Step 1 agitation stops and draining begins Step 2 as soon as the water level switch resets motor and timer stops and cold water starts filling into the wash tub until the water level control is satisfied, then step #1 repeats until the timer runs out the full two minutes. 

The actual amount of cold water used in the cool down varies quite a bit depending which model machine you have. If you have the added restriction in the drain system of the two way valve used on the suds saver models the drain flow is not as fast and somewhat less water is pumped out of the washer during the two minute alloted time. and if you have the LKM with the self-cleaning filter and the suds-saver it uses even less total water for cool-down.

We had the 1959 LKM with suds-saver for several years at my home growing up. It was the first WP built BD washer that I ever rebuilt. I did this machine around 1968 and we used the WnW cycle for all the shirts and when they came out of the dryer it looked like they had been ironed.

I used to figure that our machine used about 20 gallons of cold water for the cool-down, making the total water use around 60 gallons per load. The 1959 KM that Don has just rebuilt if it does not have the Suds-valve may use about 15 gallons more cold water for a total of almost 75 gallons per load. 

Those are nice fast dryers, I have worked with many of them. Tom and I also figured a way to make the airflow through the drum more efficient by adding two felt seals to the rear bulkhead. When you get around to rebuilding the dryer get in touch and I will tell you how to do this. Best Regards John.