There is an experimental backend of LLVM that you can try, but it will require building LLVM from source currently. Emscripten has an option to do this automatically, I believe.
You can also write the AST format by hand, which IMO is much easier to do than writing asm.js by hand, just more verbose. I wouldn't advise anyone do this, as the format has been changing over time.
Finally, there is work on specifying a true "text format" that is meant to be used with view-source and directly maps to the binary format. You can see some proposals if you look at the pull requests in the design repo. When a proposal is accepted and we implement the tooling, you will be able to generate a binary directly from this format, which will be much nicer.