Aluminum foil did not work. The fire ate right through it. Really dumb idea in hindsight, though I'd thought aluminum had a really high spalling temperature for some reason. Maybe I've been inhaling too much aluminum.
The better idea that occurred to me is just put the pot back on the rocket stove (out on the porch) afterward and don't ever touch the bottom. Just let it be permanently black with creosote or soot or whatever that is technically.
If you don't want black on the pot, we used to leave a film of soap on the bottom of our camping cookware. It scorched a bit, but it was really easy to wash off afterwards.
Tradition is not the worship of ashes, but the preservation of fire.