At this point I think current LLMs are able help these incredible feats of bootstrapping as they can grind out the impossibly long built times over multiple days/weeks.
I am very optimistic for deterministic builds in general.
In the meantime, months ago I achieved bootstrap of TCC (then GCC 4.6) via the same path as the live-bootstrap project but replacing the Scheme part with a C compiler in Ben Lynn's Haskell dialect.[1] This was a project I wish I had time to do years ago[2] but never had the time or motivation for, and the type of things agents can do well now (they couldn't write good Haskell a year ago).
[0] https://github.com/siraben/mrustc/tree/siraben/cmrustc
[1] https://github.com/siraben/blynn-bootstrap
[2] https://logs.guix.gnu.org/bootstrappable/2021-05-26.log#1438...
GCC 4.7.4 was the last version of GCC fully written in C, with full C++98/03 support and a decent subset of C++11. As far as I know it is used by the bootstrap project presented in the article.
I have no doubt that a Rust compiler can be implemented in C. But it's a different project to write one in C from start than trying to migrate an existing C++14 based project to C. The former is likely "easier". An alternative approach could be to migrate the C++14 code back to C++98 and get rid of the exceptions, which makes it transpilable to C (using the cfront approach). Though the result might not be maintainable C, but still C.
EDIT: if you manage to migrate it back to a sufficiently moderate C++11 subset, or even C++98, you could use GCC 4.7.4 to compile it, which itself is written in C.
We did that in stagex over a year ago actually and several major orgs are using it in production. Also no dependency on libgcc. LLVM native. We presented it at Open Source Summit and Linux Security Summit this year.
Clone https://codeberg.org/stagex/stagex and run "make core-rust".
Will build "FROM scratch" in containers from hex0 to recent rustc.