I don't think it's clear that the OP organisation is stuck with C. Perhaps it's the case, but I think it's also time, in 2022, to push a bit to move toward safer programming languages.
You describe an excellent set of rules and processes, perhaps too much for most projects. It sounds like it could be even better with a memory-safe programming language. Also, I doubt that most secure critical C/C++ projects proof their source code correctly in Coq or similar.
I also think many security issues are tightly related to the programming language. For example, SQL injections are because of SQL, XSS because of HTTP/HTML, and Buffer overflows because of C.
Another take away from an old old paper was that safety must be a primary design goal from the start. It's not something you can bandaid in afterwards. There is a lot of stuff out that what that didn't happen and as a result you see constant whack a mole with critical bugs.
It's clear from the OP's question that the org is already C-centric. Language support in a safety environment is a large and complex issue. The compiler, tools, libraries are also required to be validated in context (depending on the standards environment), coding and other supporting standards have to be developed or vetted for adoption, you need a population of able reviewers, interoperation between implementations needs to be validated, etc. etc. etc.
And at the end of the day, the "safety" that another language buys you doesn't actually get you very far. A lot of folks get hung up about memory safety, or this or that language feature, when in reality the majority of safety issues in large codebases are algorithmic in nature, and no low-level language feature is going to save you from implementing the wrong design.