This got me thinking. It's been a while since I did tons of this type of work, but when I did....I cut a million miles of O&G threads. And I made a ton of gages. I'll try and be coherent.
If you bought two different AWJ Pins, different sizes I mean. You could do a comparison of the 6 basic features of a tapered thread. Angle, Vanishing thread, Nominal pipe OD, Pitch, length of engagement and Pitch diameter. And determine from those factors ALL the appropriate dimensions for all the sizes. The pitch diameter is the reason it's difficult to inspect without gages obviously, but it's also difficult to extrapolate and reverse engineer the part. But not impossible. An optical comparator can get you very close, based on following the pitch line and a little trial and error. Theoretically all you need to do is match these purchased parts to the parts you're building at the comparator. I've hand made some 60° points for caliper jaws that follow the angle, I've used different sized gage pins to inspect the P.D. I've even used ball bearings and grease for the Box.
R