[RambozoClown]

Pretty much has to be a valve problem. A leak down would tell you for sure. With water in the oil, the likely issue is a stuck hydraulic lifter. If you can solve the water problem, you might get lucky and the lifters will clear on their own. A quart of ATF in the oil can help speed up the cleaning process. Otherwise, you will need to submerge them in clean oil and pump them to flush out all the gunk you got in them.

 

[RambozoClown]

The oil/water emulsion can make the lifters not work properly. Technically you don't have to remove the cams, but when you remove the rocker assembly, that is what holds the cams in place. There are plugs that retain the lifters, but I think you can't access them without taking out the rocker assemblies. You need to find out how the water is getting in there.

 

[RambozoClown]

Do a pressure test on the cooling system with the spark plugs out. See if it fails to hold pressure.