Water in oil

Make sure it is bad before a tear down. It is possible for the headers and other sources to introduce water into the oil.
I like to pressure test the cooling system with air. I know air is not hot water so the test is not exact but it rules out about 90% of the possible water leaks into the oil.
I plug all the coolant lines that exit the engine. Hook up a air source and a gage.
Pressurize the system with 30-35 PSI of air and watch what it does.
Be careful, if you pressurize higher than 35 psi you might blow out perfectly good gaskets inside the engine. They are designed to seal less than 20 psi not higher than 35 psi.
I have a ball check set up, ( home depot part ) on my set up that allows me to pressurize and then close the ball check with the gage on the pressure side, cooling system side.
Spray down your connection and all plugs in your coolant system with a mix of water and dish soap, Dawn works fine.   If you have air leaks, even small air leaks at your connections you will see bubbles forming. Make sure all connections are not leaking.
Watch the gage, If it holds the air pressure let is sit several hours.
This will let you know if your head gaskets are sealed to water, if the thermostat, water pump etc are all sealed to water. If there is a big air leak you can hear the leak. A slow leak will be harder to find.

If the engine holds air I would suspect the Exhaust headers are leaking into your heads.
I have not tried to test these for a leak but if you pull them off you should be able to find witness marks where your leak was happening.

It takes a couple hours to test but I think that is better than pulling the engine only to find no problems inside.
Hope this helps.
Mark