If a guy had mad skills, you could write a program that has each measurement co-relate to the others, to see what changing one measurement does to your total inside volume of air, and then also how much volume for air escape in the bottom holes vs. material of the pot.
Once you know the sweet spot numbers, can you then tweak one in coorelation too another and get similar final sound results. Rather than trial and error on the lathe.
Plug in a sound file for 10 different demensions, then have the computer program tell you the tuning hit, you could make these changes to hit in the middle. Plug in janko wood hardness and all.
Lol. Sounds like a crazy engineering project!