Hello, Ok well I personally have never used liquid laundry soap. I was always told and have always had good luck with Cascade powder dishwasher soap. And depending on How bad it oiled up I have ran up to a hr, each flush, up to 3 times, then straight water, then to antifreeze.. Liquid laundry soap may not have as much scrubbing power.. .. as far as the oil thermostat, its in the front of the oil cooler housing, behind that plug that faces forward, then a snap ring...
I think I would try to save you coolant and try the Cascade( I was even taught not to use liquid cascade, only powder) And change out the oil thermostat..
You are just a little too warm on the coolant, max is 225
I was looking for some good oil temp specs, but 250 I think is real close to light coming on, I think it comes on at 255.
Last is while its flushing, or even before, I would get a temp gun, and check the water jackets and radiator as its getting warm and then hot, follow the water flow from the pump see were you are heating up, make sure your water pump belt is nice and tight, and not glazed up, so you are getting max water flow, make sure heater valve is open also.. But really the temp gun should narrow it down..Hope this helps