engine code P0016

p0016 is cam to crank sensor out of sync and the only way this will be fixed is for a mechanic to hook up his scanner to put it back in sync if it can. It may be caused by a stretched timing chain or something similar to it. or maybe out of sync due to a tensioner bad. as far as sludge was the oil drained and had to take a screwdriver to get it to flow out or a valve cover removed? that is the only way they will tell for sludge or maybe they are going by seeing the bottom of oil cap when removed if it was milky/foamy then it may be a head gasket. any garage with a scanner can do the sync or timing chain fix.

The Toyota dealer mechanic removed the valve cover to exposed the sludge buildup so the question remains, can I have the sludge dissolved with a chemical flush to the extent that is wont be a risk of plugging the oil pickup line?

It would probably plug the pickup if you flushed it if sludge was really built up around the valve springs that is very poor maintenance like never changed since two to three years of driving. if just a little bit on head do not be to concerned with it just do a better job of changing oil and filter like very four months if not driven a lot or short hops like less than ten miles always or 5000 miles if driven over that.