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...