The thermostat will be fine.
Pull the lower radiator hose for faster draining.
Did you find and fix the source of the oil contamination?
Fleetguard has Restore and Restore Plus. It sounds as though Restore Plus is better suited for your heavy duty cleaning needs.
Restore is alkaline based, same as dishwasher soaps. The down side of automatic dishwashers soaps is they contain a very high amount of grit. That's how the dishwasher gets the food particles off your dishes. That grit is not good for the inside of your engine if it is left there.
Do not let your cooling system dry out unless all the scale and silicate gel is completely flushed. Once they dry out, it is nearly impossible to get them out even with repeated flushings of the system.