I am not much of a Zig-head, but the best compromise I can think of is having a few operators which purely and solely exist for this purpose. In other words, there is no operator overloading, but you can define, say, "#+" for any two structs, or something like that.
So if you want to encode matrix multiplication, then you'll always have to write `mat1 #* mat2`. This feels like a hack, and isn't all that elegant, but it'd be clear that every usage of such an operator is a disguised function call. (And according to what Andrew Kelley said, it's all about not hiding function calls or complex operations in seemingly innocent 'overloaded' symbols.)
If you want to take this one step further you'd probably have to allow users to define infix functions, which would be its own can of worms.
Honestly, I am not particularly happy with any of these ideas, but I can't think of anything better either!