It make take several goes , but a friend who used to specialise on Rover 400 head gasket jobs when they used to fail for a past time suggested dish washer tablets, warm engine carefully add tablets or similar liquid, top up coolant and run for 10 minutes or so @ around 1500/2000 rpm keeping an eye on temperature etc. then drain and repeat as necessary. Note don't leave in system, it will need flushing out properly, if using cold water to flush only do when engine cool to prevent damage!
Once system is as clean as possible then replace normal antifreeze etc. It is nearly impossible to make it 100% clear of oil, but this isn't bad.
The other problem is making sure the thermostat is open when tablets put in to ensure all the system is treated, so ideally do with thermostat out if possible. Note my friend swore by this method and I have used it successfully, but at the end of the day it is only a suggestion , so at your liability.