I’ve never used ATS to do what the GP is suggesting of incrementally wrapping C with proofs, but I can’t imagine this being simpler than just rewriting the C in Rust. You wouldn’t get the same proofs, but you would get memory and thread safety, which for many apps would be an incremental improvement.
I haven’t taught ATS, but I found it harder to learn than Idris, and I can’t imagine C programmers which have a hard time with Rust learning it quicker than they would learn Idris or Rust.