You definately don't want oil in your cooling system. There's nothing you can add to help with contamination, you'll have to flush the system.
Since you're taking apart your engine, you can do this while your car is apart.
Take out the radiator and put a running hose on the top and wait till it's all clear water running out, then tip it upside down, and repeat as necessary. On the top end, take out the thermostat and then lightly bolt the housing back on without the thermostat inside. Run water through the upper hose like a funnel and watch the water come out the bottom hose until it's clear as well. While you're doing this (take off the serpentine belt and fan blade until only the pulley is left on the water pump shaft and tighten the bolts so you can turn the water pump) and turn the water pump while flushing water through the engine, maybe this won't do a thing, but it may cause crud/oil to leave the water pump passages or in spots trickling water may not hit.
You may have to flush it again after doing this to make sure there's nothing left but this should take care of nearly all the crud (i did that in my car and now my car has winterfresh green coolant instead of a heavy yellow/orange rust). Good luck.
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'84 Mustang 5.0 LX
My car