Honestly the amount of effort to try to reverse engineer all this is much more than just using a solid test routine.
A material test for cutting will take only a couple minutes, and engraving is so complex and subjective that in my eyes there’s no such thing as a “right” setting.
I just posted a proper write up of how I test. Might be worth trying if you haven’t?
I think you’ll find that materials vary so much that it’s just faster and easier to test them as you go.