I was looking at some aluminum channel today and the light bulb came on-- a channel with a base width of about 2.5"/64mm (approriate to the pot you want to use) and legs the same height as the Esbit folding stove legs at the 45 degree setting. With a metal cutting saw you could turn out a dozen stoves in a few minutes. I would expect to spend more time deburring the edges than the cutting. It would make a super stable pot base and would fit in your pot.
A little more cutting could relieve the closed sides, allowing a more even flame pattern, better air flow, and less weight. With access to a simple milling machine, this could really be a sweet little pot platform, but a bandsaw or even a hacksaw and drill could turn out a decent one-off--- you could file away the imperfections. Form the same thing out of titanium sheet and it would be tough, take more heat, and be super light.