limestone and plant glue

Your alternative recipe would still share the limitations of a traditional chalk gesso, which is only recommended for inflexible supports like panel, and never for stretched canvas as it is far too brittle. Better might be to try using sodium carboxy-methylcellulose  (CMC) as a size directly on the canvas and then use a lean oil ground on top. You might need to experiment with the number of coats you apply to the canvas, and the ratio of the methyl cellulose to water (an 8% solution is a good starting point). CMC is used as a sizing in the textile industry, as well as papermaking, and while often mentioned as an alternative size for people wanting to avoid animal products (as well as PVA/acrylic). I am not aware of long-term studies or conservation research around the use of CMC as a size for oil paintings, so it might still need to be considered experimental, but the conservators on MITRA might be able to chime in on that.

​I agree with Sarah, I can imagine this material proving adequate as a panel sizing but formulating a “gesso” with an experimental binder would require significant testing. I did locate a blog post by an artist who seems to have tried something similar to what you are proposing:  https://dbclemons.wordpress.com/2017/10/01/testing-gesso-made-from-cellulose-gel/

Also, a company called “Natural Earth Paint” (mentioned in the above-linked post) apparently sells a ready-mixed cellulose gesso. Maybe you can reach out to these resources and ask if they can share any detals of formulation.