While ZDDP is a good thing to some extent for these cars, some of the specialty oils - some of them meant for racing - go overboard and it has become a marketing buzzword. The stuff is there for wear protection but there are compounds other than ZDDP present in the oil for that purpose as well. I understand that too much ZDDP (phosphorous and sulphur rather than the zinc are the actual anti-wear components) can cause ash buildup.
Particularly with break-in or running in oil, some is good but it should be less than in the regular oil you use later on. Too much ZDDP will interfere with the purpose of running an engine in, which is to allow the machined surfaces of new parts to mate properly in order to form a better seal and lubricating surface. That's also why you don't want to use synthetic oil for running in. It is too slick, will not allow proper mating and will form a glaze which will be counterproductive to good lubrication later on. After market ZDDP additives may be tricky too, in my opinion. Good oils with ZDDP included have the other protective additives balanced to compliment the ZDDP. That balance might go out the window when using an additive applied after the fact.
One more observation about running in oils. I have checked out numerous products here and abroad. Two of the UK's major independent oil companies that cater to classic cars with special lines of oils use less ZDDP in their running in oils than do the US products I have checked. Mainland european companies I contacted are no higher, perhaps a bit lower, than the US. A major Aussie company, on the other hand, goes a bit higher with its ZDDP. Concerning the UK based Castrol Classic oils now available in the US, I have never gotten an answer from their customer service folks concerning ZDDP content; in fact, no answer at all.
For those who really want to get into oil, here is an interesting read:
https://www.amazon.com/Which-Oil-Ch...UTF8&qid=1438878985&sr=1-1&keywords=which+oil
Regards,