It would also be nice to publish pre-built binaries, considering that the build requires a very specific version of the Rust toolchain that users are unlikely to have installed.

I haven't thought much about publishing binary distributions, but one complication that I foresee is that mir-json's binaries are implemented as rustc/cargo plugins. My understanding is that plugin-based tools are intimately tied to the particular toolchain used to build them, and as a result, I'm unclear if you could simply download and run mir-json without having the parent toolchain already installed. (I could be wrong on this, however—I haven't tried to see what would happen.)

I'm unclear if you could simply download and run mir-json without having the parent toolchain already installed.

You do need the parent toolchain. The various mir-json binaries link against that toolchain's specific versions of libstd-xxx.so and librustc_driver-yyy.so.

I believe Kani handles this by shipping the toolchain itself along with their binaries that depend on it.