Use regular oil. If the motor is put together properly there is not much that can go wrong.
ZDDP has been REPLACED with other additives that work just as well, but use other compounds.
There are lots of motors made today, that use flat tappets, and come from the factory with normal oil.
Company like Amsoil and boutique oils need you to believe that ZDDP is magical unicorn pee so you buy their stuff. Professional re-builders use it because of the misconception that its still needed. Plus they can mark up their 'special blend' of break in oil and (wait for it) sell it.
Use what you like.. I'm sure that when we are all in Mr. Fusion powered DeLorians someone is still going to say that you need ZDDP to travel time faster.