You can go too far with adding ZDDP, and it's been proven that more, isn't better. When there is too much ZDDP in oil it will have an adverse effect and actually cause scuffing components (flat tappet cams and lifters) to fail prematurely than the same base stock oil with less ZDDP in it.
I doubt that running diesel oil is going to cause flat tappet cam or lifter failure by itself, but I won't say it couldn't happen, cause I really don't know myself. Now ramp up the levels of ZDDP more than what the oil company puts in it when it's formulated (additives) and you can be running into problems that too much ZDDP causes.
Diesel oil has to deal with many times the amount of soot caused by a higher volume of blowby due to compression ratios near 18-22.5 to 1. and a fuel that doesn't burn as clean. Gas engines have soot too, but not anywhere near the volume in diesels. Stands to reason that the soot element alone is going to cause a different formulation of oil. Can the oil be interchanged on a gas engine? better to ask the experts from the oil manufacturer, than the experts on the internet
Most brand name oils made today have started using other friction modifiers because the feds wanted ZDDP cut back. If you do some due diligence you'll find that there are other chemicals that oil manufacturers can use to supplement the oil in a flat tappet application.
FWIW, if you really want to know what works for your application, don't ask on forums. When I have a lubrication question I simply call the oil companies tech lines. They know much more than anyone on the internet knows about their own products.
I had a problem in an air cooled application that kept seizing the pistons on a parking lot blower, causing it to break the connecting rod at high RPM. I called Pennzoil, gave them the rundown of the problem and the application. They recommended their 10W30 synthetic and the engine never tossed a rod after switching. BTW this was when synthetics weren't common place, and they were very pricey.
I know that no one wants to hear this, but one of the biggest enemies of engine oil and engine longevity is the junk filter system Detroit engineered. Just installing a better filter system is going to at the very least double the longevity of your oil and engine, likely 3-4 times over a standard filter system.
When you start removing solids from the oil 20-40 times smaller than the regular oil filter is designed to catch, it makes a huge difference. I didn't believe it until I switched on my own stuff, it flat out works exactly as advertised. The under 10 micron stuff is invisible to the human eye, but your engine knows it's there, silently wearing the internally oiled parts prematurely.