This is a new thread from posting on May 2, to avoid confusion (for me!)...
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First guess is the rings on #3 have failed, thus the oil. You didn't mention smoke from the exhaust or anything about coolant, so I can't be more specific. Either way, I'd remove the head. If the rings need replacing, it can be done on #3 without removing more than the head and oil pan (I've done it), i.e. the engine can stay in the car. This will allow for direct inspection of all the cylinders, walls, and the bottom of the head and valves. You'll be able to replace nearly anything you need to at this point. New: head gasket, head bolts, rings #3 (they come as a complete set and I might just do them all to be safe since it's open), valve cover gasket. Check the timing chain guides or belt and tensioner, intake-to-head gaskets if removed. Maybe do the water pump and gasket. No need to replace the engine. They are built pretty well and this should be rebuildable easily. You will see the cause of the problem when the head comes off. Unless the rings gouged the cylinder wall or ruined the piston top (doubtful), this should be basic R and R. You may need the cam holding tool for the head removal. Time consuming but not hard, and uses basic tools. Get access to a Bentley manual first. Oh yeah, what about coolant system?
Bill in Omaha '86 535i