Metal in oil

I formulated automotive engine oils for Chevron for 18 years so I know a thing or three about oils.
Engine oils are complicated mixtures of dispersants, detergents, antiwear additives, antioxidants, friction modifiers, antifoam agents and sometimes other components. Getting the formulation out of balance by adding supplements to the oil can lead to problems and will definitely void the engine oil producers' warranty that the oil will not cause engine damage (a very common claim of essentially all major oil brands).
ZnDTP (Zinc, ZDDP, and other names) is a sacrificial antiwear additive. It works by bonding with metal asperities at highly loaded surfaces (e.g., camshaft and lifter) forming a Iron-Sulfur-Phosphorus surface that very gradually wears away and is replaced by more Fe-S-P surface. This mechanism prevents what is termed spot-welding wear where asperities micro-weld to each other pulling material from the surface leading to catastrophic failure.
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From Wiki, but there are other sources describing what is going on.

The oil is formulated to minimize this micro-welding wear using engine tests that scientifically measure wear in standard tests (and they are incredibly severe standard tests). For slider follower camshafts, about 12 millimoles of P (a measure of the number of Phosphorus molecules) of the right type of ZDDP (yes, there are different types that work in different applications).
The point is, more of a good thing may be too much of a good thing. So adding a supplemental ZDDP to an oil that has the right amount already may actually increase wear or deposits defeating the purpose entirely.

I would recommend using a top brand oil that is formulated for older cars (there are many available from Valvoline and so many others) and changing the oil at no more than 3,000 miles.
I ran taxicab testing on very old API SF oil (meeting late 1970's specifications) in NYC Taxi Cab Testing at 3,000 mile drain intervals. At 100,000 miles of the worst type imaginable (NYC Taxi's), this oil outperformed much more modern formulas, including Mobil 1 and other synthetics, in all aspects of performance. Sludge, Varnish, cylinder wear, cam wear, were all better with the shorter drain interval compared to using the "Best" oil at longer drain interval. This proved that oil drain intervals and using an OK oil will protect your engine better than using a high-quality oil but not changing it as frequently.
Sorry for the long post, but there is a lot of science here that debunks many advertising claims from especially oil supplement producers.