TypeScript: Using a condition mapped type on a type that extends another type causes error

TypeScript Version: 2.8.1

Search Terms: conditional types, extends

Code

// A *self-contained* demonstration of the problem follows...
interface StringOption{
    type: "string";
}

interface NumberOption{
    type: "number";
}

type ValidTypes = {
    [key: string]: string | number;
}

interface ISampleObject extends ValidTypes {
    stringParam: string,
    numberParam: number
}

type MappedOptions<T extends ValidTypes> = {
    readonly [P in keyof T]: T[P] extends string ? StringOption : 
        T[P] extends number ? NumberOption : never;
}

const mappedObject: MappedOptions<ISampleObject> = {
    stringParam: {type: "string"},
    numberParam: {type: "number"}
}

Expected behavior: This should compile correctly

Actual behavior: A compilation error is shown:

Property 'stringParam' is incompatible with index signature.
Type '{ type: "string"; }' is not assignable to type 'never'.

Playground Link: Playground Link

This code sample works fine if the ValidTypes type is removed. I am using this type to limit the property types that can be used with this mapped type. Without it any type could be used and complex types containing functions and booleans could be created.