[ChrisRackauckas]

>Is there any sense in trying to go all out and write my analysis code in Julia or Numba (via Python), and spit out the LLVM IR to feed to Emscripten and compile to JS?

Julia is working towards something like this. This GSoC project description is pretty clear about the current state of web assembly:

https://julialang.org/soc/projects/general.html#webassembly

[MooMooMilkParty]

I hope this capability gets to maturity. It consistently seems like anything I want in a language is in progress in Julia; new scientists in 15 years are going to be very spoiled if Julia becomes mainstream.