Example using bazel with a non-system compiler and crosstool
I copied from bazel's bazel_toolchain_test_data, which uses a linaro arm compiler, and substituted an amd64 compiler. I tried one from bootlin, but its gcc was named gcc.br_real which caused problems. Fixing the archive and re-creating may have fixed it, but I felt I'd have more luck building a toolchain with crosstool-ng (documented below).
This doesn't do much! But if you want to try it, install bazel, clone the repo, and then run ./run.sh. That will download the 120MB (!) toolchain, extract, and compile the hello world demo.
Included for completeness. Bazel will download the tarball to its cache.
The config file here works with crosstool-ng rev d7eed4ee52a793. I cannot guarantee that it will work with other versions.
# note that you will need to adjust paths if you do not run these commands starting in the bazel-amd64-crosstool dir!
git clone https://github.com/crosstool-ng/crosstool-ng
cd crosstool-ng
git checkout -b bazel-amd64-crosstool
git reset --hard d7eed4ee52a793
./bootstrap
./configure --enable-local
make
cp ../crosstoolng.config .config
./ct-ng build.`nproc`
# this will take a while
tar cJf ~/x-tools/x86_64-unknown-linux-gnu-gcc-730.tar.xz -C ~/x-tools/ x86_64-unknown-linux-gnu