How can I build self-hosted clang in nix?

I’m trying to build a self-hosted clang in nix.

By reference to other pages (NixOS Wiki: Using Clang instead of GCC) and threads (Nix discourse: Use Clang without GCC’s C++ standard library), I tried (variations on):

nix-build -E "with import <nixpkgs> {}; pkgs.clang-tools.override{ stdenv = pkgs.clangStdenv.override (x: {cc = x.cc.override(_: {libcxx = llvmPackages.libcxx;}); }); }"

But this appears to not be working:

$ nix-build -E "with import <nixpkgs> {}; pkgs.clang-tools.override{ stdenv = pkgs.clangStdenv.override (x: {cc = x.cc.override(_: {libcxx = llvmPackages.libcxx;}); }); }"
/nix/store/45whyxm1y5mjf5g12c0wjvjcmrxxqdaz-clang-tools-10.0.1
$ tail -n 1 /nix/store/45whyxm1y5mjf5g12c0wjvjcmrxxqdaz-clang-tools-10.0.1/bin/clangd
exec -a "$0" /nix/store/6pzqj9q656vc1msa675k75hmhsrfizsy-clang-10.0.1/bin/$(basename $0) "$@"
$ ldd /nix/store/6pzqj9q656vc1msa675k75hmhsrfizsy-clang-10.0.1/bin/clangd | grep gcc
libstdc++.so.6 => /nix/store/c10296m7xgm3ksibcklb2xf48jr635x3-gcc-9.3.0-lib/lib/libstdc++.so.6 (0x00007f55d359b000)
libgcc_s.so.1 => /nix/store/0c7c96gikmzv87i7lv3vq5s1cmfjd6zf-glibc-2.31-74/lib/libgcc_s.so.1 (0x00007f55d343e000)

Am I missing a step? Or mis-interpreting the output of ldd? I realize that clangd is itself a script, I did reproduce the environment that creates, but it makes no difference (and I wouldn’t expect it to). I’ve excised that from my example above for simplicity.

This technique appeared to work with powertop, so maybe clang-tools is special in this instance.

I tried also building nix-build -E "with import <nixpkgs> {}; pkgs.clang.override{ stdenvNoCC = pkgs.llvmPackages.libcxxStdenv; }" with similar results.