Classic Car Club of America contracted DA Lubricants, the makers of Penn Grade, to formulate oil for flat tappet engines.
It has 1600ppm ZDDP and is sold in 15w-40 weight. And it's only $7.00/qt instead of $9.00.
Classic Car Motor Oil
https://inrccca.org/product/classic-car-motor-oil/You're correct about the zinc additive not mixing correctly with the oil. There is no possible way to ensure that an additive is evenly mixed in the crankcase. Of course every time you have to add oil to top up the level, you dilute the mixture anyway.
It makes more sense to buy oil formulated for the job you desire than to try and mix up a home brew yourself.