With the weather forecast showing that we'll be getting our first freeze tonight I had to relent and replace the water/soap with anti-freeze/soap.
The seventh drain was 90% clean water. There was oily sludge in the coolant overflow bottle like always, albeit less. I put in some Peak brand anti-freeze and I am hoping to get one last time to perform an eighth drain / replace before winter officially sets in.
I feel good about the progress I've made so far. I plan to run the same radiator and hoses over the winter. In spring I'll do another 1-2 drains and replace the radiator, hoses, and finally get the oil leak figured out -- the original point of this thread in the first place!