Thanks for the writeup! I had a hard time figuring out how to compile C++ to WebAssembly a couple of weeks ago and finally gave up given the lack of maturity of the implementation. I am sure this will help more people get interested in WebAssembly!
I had the exact same problem when I first started. Someone once told me "what we can throw away to solve this problem", so I kept removing parts until I got here which I think is currently the easiest way to get started.
Ultimately you should be able to use your C compiler and generate wasm files directly, rather than go through asm.js.
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.
I'm familiar with the LLVM direct to wasm tool, but I was unable to get it working using the steps from the emscripten docs. The binaryen toolchain is pretty easy to digest, but I've been using the emsdk almost exclusively for the convenience. Once you have to rework part of it from source, I just don't know enough about it to debug it yet.
Thanks for the info on where to find outstanding proposals.