Hi Paul!
I missed the screwdriver reference when I quickly read through your post!
I know some are recommending a thinner oil - however, a thinner oil will not help the situation.
As you specifically noted in your original post, you state:
It worsens as the oil temperature rises and is not even noticeable when the engine is cold.
The reason being is that due to the oil being cold, the oil is actually thicker prior to warm up or normal operating temps. Sometimes thicker oil can mask certain internal engine noises, reduce blow by, etc. Some shops will recommend or use a thicker oil in higher mileage engines due to internal wear on bearings, lifters, rockers, rotating assembly, etc. As you note, as the oil warms up, the noise is more present - even when using a 15w50 oil. Using a thinner oil will not help nor solve the issue you are experiencing. In some areas of the country, especially those that experience Winter, using a thicker oil is not good because the thicker the oil is, especially when at or below freezing temps, the longer it takes for the oil to reach all of the parts that need to be lubricated appropriately.
Usually, in winter months some folks go with a thinner weight oil and in summer months most folks will go to a thicker weight oil. This is for those w/ higher mileage engines - I'm not saying this is the thing to do for everyone, but it does work in instances where these engines, regardless of vehicle type, do benefit from the different oil viscosities during Seasonal changes. Some use a thicker weight oil all year round, however, if or at below freezing temps, this is risky.
Have you ever heard or read up on "SeaFoam"? I have personally never used the product, but have read about it on multiple car forums (every forum from BMW, Toyota, Honda, Volvo, Fords, GM, etc) and based on the responses and very lengthy threads, some folks swear by the product after using it. It's a product that the engine "injests" internally and the product is supposed to thoroughly clean out the engine internals from any varnish, carbon, "gunk", buildup, etc... Many have reported that after using the product, their engines have run much better, gas mileage has improved and even those that had some minor internal noises, the noises have been non-existant afterwards (such as stuck lifters & lifter ticking). If you have not read up on the product, just do a search on any automotive forum you belong to (or google it) and there's plenty of info on it which may help you too.
I'm going to say that the ticking you are experiencing could be worn lifters. Once the oil has been heated or reaches optimum operating temp, it is thinned out a little and the lifters will be ticking more so than when the oil was cold & thick. Remember, lifters are pressurized by oil - the denser the oil, the more pressure being exerted into the lifter - when the oil thins out, there is less pressure and less pumping of oil out of the lifter, especially on worn lifters (or higher mileage lifters).
There is a distinct difference between a tick & a tap. Usually ticking sounds like an old sewing machine. Fuel injectors do tick as well - on some vehicles the noise is more prevelant and louder than others (due to engine design & injector location), it's just the pulsation of the injector function.
At what spots or locations on the engine have you used the stethoscope method? Did you try it at each injector? How about along the intake runners? How about on either side of the valve cover or at different spots along the top of the cover?
