String literal type inconsistency in overload resolution

As far as I see, the TS compiler still sees a string literal type of a single literal as an old style "string parameter" thing. I thought that the concept of string literal types should replace overloading on string parameters, but seems that it doesn't.

That complicates things, and results in a "strange" behaviour in overload resolution:

class A256 {
    m(a): any;
    m(a: "a" | "b"): string;
    m(a: "c"): string;
    m(a): any {}
}

var foo1 = new A256().m("a"); // 'any'
var foo2 = new A256().m("c"); // 'string'

What should be the correct logic with string literal types in overload resolution?
Shouldn't overloads with unions of literals precede the others as well, when resolving overloads?

Start by compiling the A256 example and compare the inferred types of foo1 and foo2 with the expected overload behavior. Then trace the compiler's overload-resolution handling for string literal unions; done means the behavior is defined and the example resolves consistently with that rule, with regression coverage added if the relevant test location is identified.