Another oil option is buying racing oils, such as Valvoline Racing Oil, Joe Gibbs, or Brad Penn. Look for a label that specifically states something like "contains added zinc." It may also state "not for passenger cars" and explain that it may damage catalytic converters. This is not a problem for pre-'75 cars or other vehicles that don't have a catalytic converter.
Another option is buying from a specialty oil company that formulates oil with antiwear additives similar to the good old days. Call them with a credit card and they can ship oil to your door.
The second way is to supplement modern oils by pouring in a break-in additive from a camshaft manufacturer at each oil change. These can be ordered from cam manufacturers, from speed parts distributors such as Summit Racing or Jegs, or picked up at local speed shops. Because formulations change, the safest policy is to check with suppliers of diesel oil, racing oil, or cam break-in additives to learn the current concentrations of their antiwear additives.
There are two sides of the argument about the danger of running synthetic oil in a flat-tappet cam engine.
The pro-synthetic oil argument is simple: thousands of people have run synthetic oil in flat-tappet motors with no problems (yet). But remember this is anecdotal; there are no long-term real-world tests across a variety of engines, and almost certainly there will never be any. Plus, just because many have run synthetic oil without a problem, that doesn't prove there isn't a higher risk factor.
The "be wary of synthetic oil" argument has a couple facts. First, we know that synthetic oil is more slippery than conventional oil (which oil-heads nickname "dino" oil for dinosaur). This sounds good but actually may not be good for flat-tappets. For some background, flat-tappets are not completely flat. They have a very slight crown ground into their face. Also, each cam lobe is slightly tapered toward the front, and the lifter bore is slightly off-center on the cam lobe. These three things are done to make the lifter turn when the cam lobe slides on it. If the lifter stops turning, the cam lobe wears on the same area of the lifter and both wear down soon thereafter. Synthetic oils are so slippery that there is less force to turn the lifter. So, theoretically, synthetic oil could cause problems for flat-tappet cams.
The real-world warning comes from cam manufacturers. Who has better experience than the people who make cams, test them, and learn of failures because they warranty them? Major aftermarket cam manufacturers state not to use synthetic oil during break-in, and one states not to use synthetic oil for at least 5,500 miles after break-in of flat-tappet cams.
This writer switched to synthetic oil well after break-in, and subsequently lost a cam lobe at 4,500 miles. Inspection of the wear pattern on the other lifters showed three that were not turning.
Amsoil, the inventor of true synthetic oils, is aware of the flat-tappet cam problems and offers several oils with high phosphorus levels (over 1,250 ppm) and zinc levels (over 1,350 ppm). AMO 10W-40 and ARO 20W-50 Synthetic Premium Protection oils are recommended for flat-tappet and late-model high-performance motors. Amsoil's TRO 20W-50 Premium Synthetic Racing oil is recommended for highly modified, high-horsepower street or race motors. AHR Synthetic SAE 60 Racing oil is recommended for nitro- or alcohol-burning motors to protect from oil dilution by fuel. HDD Series 3000 Synthetic 5W-30 diesel oil also offers extra protection from high soot loading and acid generation in modern diesel engines.