Try buying 20 lbs of calcium hydroxide, it is sometimes used for soap making iirc, so it should be available on amazon. Bubbling air through a concentrated solution should do something. At least at the CO2 concentrations of exhaled air you get visible amounts of insoluble carbonate: https://www.youtube.com/watch?v=Vl9A8Iyc_LY
My literature searches haven't had much success thus far, lacking a chemistry degree hasn't helped. I have found some things but not enough to come to any sort of engineering designs. I'm assuming it's one of those things that's almost too simple for anyone to have bothered writing a paper about unless they had the exact sort of ideas I did. (OR they're using terms that I haven't been able to come up with yet)