Update: The Rust LLVM upgrade finally landed (thanks @jer and everyone who helped - it was a brutal slog).
Next @kripken is going to upgrade the emscripten incoming branch to the same merge base. But we don't need to wait for that probably. He's already prepared a rebase that should be in the ballpark of the same commit: the fastcomp next-merge branch.
So our next step is to take all of their patches, apply them to our tree and merge that into Rust.
Unfortunately, there's a gotcha - @kripken didn't realize that our plan was to apply the emscripten LLVM fork to all of our targets and he's a bit worried about it. The reason is that the fastcomp branch is only tested for the emscripten target, and it's based on the old pnacl fork, which has a bunch of ancillary patches of unknown value. So we may run into unanticipated problems (and in fact last time we had this working the x86_64 backend miscompiled things).
Furthermore, the fastcomp history is lengthy and messy, with all that pnacl legacy. So we are going to need to scrutinize it carefully and see e.g. if it's doing anything to the x86 backend. We might, e.g just squash their entire history into one 'emscripten' commit, then revert large chunks of it. It could be a big mess. (We also have the option of pursuing a strategy where rustc can optionally use an emscripten-specific LLVM).
It's also worth noting that the upstream LLVM wasm backend is still in progress and the last I heard the wasm team is trying to have it ready for the wasm launch late this year. So the longer this process goes on the more likely we are to just end up on the upstream wasm backend and skip the asm.js backend completely. Still, I think it's worth continuing on the path we're on and seeing how far we can get.