Comp,
The general consensus seems to be that flat tappet engines need at least 1200 ppm of zinc dithiophosphate (aka zinc). It's hard to find such an oil in a normal retail parts store, but these should still be ok:
1) Chevron Delo 400le (non-synthetic), 15W-40, CJ-4 API rating, 1230 ppm zinc.
2) Valvoline Premium Blue (non-synthetic), 15W-40, CJ-4 API rating, 1291 ppm zinc.
I sure there are some synthetics with more than 1200 ppm of zinc and hopefully, someone else will chime in.
Hope this helps.