To answer my own question, this appears to have been disabled because it's broken since LLVM changed repository layouts...?
However it's possible to build LLVM oneself, something like this:
cmake \
-DLLVM_ENABLE_PROJECTS="clang;lld" \
-G "Unix Makefiles" \
-DCMAKE_INSTALL_PREFIX=/opt/llvm \
-DLLVM_TARGETS_TO_BUILD='WebAssembly;X86' \
../llvm
(I used /opt/llvm as the target path, you may choose another.) Note I had to explicitly enable the 'lld' project to get the 'wasm-ld' linker to install.
Then do make && make install with suitable parallel jobs option in -j (-j12 on my 6-core/12-thread laptop).
Then set the LLVM_PATH in ~/.emscripten, and I also had to add it manually to PATH.
Now run the rest of the build as usual, with the new clang/llvm/wasm-ld/etc being picked up automatically.
-- brion