Is this really a useful application of function overloads? Integer promotion is tricky as it stands. Overloading, instead of having the user signal intent explicitly, might increase likelyhood of errors, and make them harder to find.
But think about all the callers of these functions. There are usually more callers, at disparate places, and context will be less narrow there. It's important not to conceal what is intended to happen at the call side. If these functions are overloaded and at some point due to unexpected integer promotion or a crazy typedef the wrong overload is picked, you will have a hard time debugging.
How you wrap those implementation things, is up to you. I agree, overloading might have problems.