I'd honestly just start with musl libc. The one Emscripten supports mostly just imports the same syscalls as Linux, with some ugliness to be able to do some DCE. If you clean that up your embedder will only need to implement those syscalls.

I am working with musl, however not the one with emscripten. That one is heavily modified farming out significant parts to the javascript runtime. It is a goal to provide a minimal surface area for embeddors and part of that is not requiring a JS runtime.

Please contact me privately. My email is in my profile. Thanks!