I've always undone as much as poss and shoved a hose in
Unfortunately won't work for oil contamination as the oil sticks to the surfaces inside.
Open the drain and take the header cap off .. allow as much out as comes, close drain, fill with a pre-mixed low suds biological detergent /water mix, with heater on max hot run engine with header cap off "burping" the pipes to remove air, allow to get pretty warm but watch for overheating .. just in case oil has blocked any waterways.
It is important that the engine gets hot, as a) the thermostat must open to get circulation, b) the detergent works better when hot, switch off and leave to stand for 30 minuts at least.
This further alows the detergent to do its thing and also prevents any "hot spots" caused by residual heat and no coolant, which can happen if you drain straight away. Drain.
Repeat ... at least a dozen times if not more ..

When I did my mates 2.2 we were lucky .. his missus had acess to large quantities of commercial strength low suds biological detergent ....

Still took over a week doing the procedure 3 times a night !!