OPE engines are not different in fundamental designs and operations like ordinary gasoline Normally Aspirated spark-ignition engines.
So, what goes and works well in automotive gasoline engines will work just as well in OPE engines.
In the case of B&S flathead engines, the design (flathead, with side valves) is so old, it dates back to Ford model-T era. It's low compression (less than 7.3:1 compression ratio) and the rest of the designs in pistons, rings, etc. are the same as automotive engines of yore, it just means that automobile oils will definitely work on them.
Just because B&S and the likes does not have the kind of additional R&D money to devote into lubricant (and they would re-use/refer to older or other lubricant specifications as their form of reference to use in their OPE engines), meaning that they would simply recycle materials from some 30+yrs ago or even older, just because it "works" before.
Think of it this way: modern NA gasoline engines are on API SN grade already, with much higher compression, OHC, high revv, etc. and yet they can still last hundreds of thousands of miles using this "reduced ZDDP" oil grade, in that sense, you think your engine would be drastically shorted it's service life with those low compression, low valve spring pressure, plastic cam type OPE engines just because of the reduced ZDDP contents?
Mind you though: ZDDP doesn't "adhere" onto plastic cam lobes.
The only concern on OPE engines are typically air-cooled, and will require a slightly thicker oil viscosity type to keep it from "boiling off".
Just use whatever your heart's content, and never lose sleep over the additives part.
Q.