Necroposting a solution I’m mostly satisfied with.
Basically the solution is to create the document with Typst.
You can use the Typst Jlyfish package to run Julia code in your document during the document development. The code and its results are cached to reduce unnecessary code re-runs.
The VS Code Typst extension enables essentially a linearly-executed reactive document preview session.
And Typst has excellent math syntax, arguably better than LaTeX, at least for me.
Compiles faster than LaTeX too.
There are few small issues with it, but all of them are acceptable tradeoffs when compared with the alternatives.