The level of ZDDP needed is directly proportional to the valve spring pressure. Here is a reference to the definitive article on this subject: "In a SAE paper titled "How Much ZDP is Enough?" from 2004, the resulting trend of decreasing phosphorus is as a direct result of observations that modern engines, with lower spring pressures and lighter valvetrain, including multiple intake and exhaust valves, seems to require only .03% Ph to prevent wear. It was further documented that by increasing to 180 lbs of spring pressure with a .03% ZDP resulted in 267 mil of wear where with .05% ZDP concentration tests resulted in 26 mil of wear. That same .05% oil with just 205 lbs of pressure resulted in 153 mil of wear, requiring .095% ZDP to reduce wear, resulting in just 16 mil. The ZDP requirements of a motor oil are directly proportional to valvetrain spring pressure."
I don't have personal experience with stock flathead valve spring pressures but my researce indicated that such pressures were in the neighborhood of 70-120 lbs of pressure. If that is correct, then, according to the above article, at that pressure, something between .03% and .05% concentration of ZDDP would be adequate to substantially reduce wear. Inasmuch as most modern API-SM rated oils have that concentration, it does not appear that any added ZDDP supplementation is necessary, at least with fresh oil. However, studies have also showed that ZDDP concentrations up to .20% do not have negative impact on wear rates. So, ZDDPlus, which I use, that adds 1200 ppm to API-SM's 600 ppm totalling 1800 ppm is not detrimental, but apparently not necessary, at least not when the oil is new. What I could not find is the rate that the ZDDP depletes over time (because it is actually used up on the wear surfaces) and whether it might get too low before the next oil change if the oil alone just barely had enough to start with.
Even though it doesn't look like I need to supplement current oils with ZDDP at the oil change, just to be sure that there will still be enough ZDDP left by the next oil change I will probably go ahead and keep adding ZDDP, but in smaller amounts, just to be sure.
I've learned much today studying this out and feel that I have reached the correct conclusion on this matter. It is different than what I thought before.
Caveat: This conclusion is for ongoing, long term oil use with stock setups - not break in use nor higher than stock valve spring pressures which require much higher levels of ZDDP. That's another subject for another day.