sadly no, modules won't solve this problem. Yes you can write your implementation in a single module but it'll behave as if you were writing them in a .h file. That means that changing a single number in a module will trigger a recompilation of all the dependent modules. At the end of the day you end up with slower compile times for small changes. I was hoping to finally be able to be done with header files but no.. another missed opportunity for C++. Perhaps future C++ compilers will be able to figure out if the external surface of a module has actually changed or not and make this possible.. but alas it doesn't seem to be the case in VS2019 at the moment.
Or use traditional C. The x86_64 System V ABI is well defined enough that I'm honestly not sure why we need prototypes. All we need is a compiler that authorizes us to use an ILP64 data model. Then we'll be able to write C the way it was intended to be written without the quadratic header complexity. C++ showed us where that path leads and I truly hope modules happen but it's about as likely as my hopes of restoring the good parts of K&R C.