In your case it would be more like "adding" a make-like tool to tie all the steps together rather than "switching away" from anything.
The tool I have in mind is buid2[1] (full disclosure: I work on the project). In this context you would be using it as a portable (and saner) make replacement (though we do have a Rust module in the works but that is geared more toward multi-language C/C++ and Rust builds).
In fact, if you are interested, I am prepared to put my money where my mouth is and code up a demo/prototype for you (without any expectations that the result will be used).