C# – n alternative to bastard injection? (AKA poor man’s injection via default constructor)

I most commonly am tempted to use "bastard injection" in a few cases. When I have a "proper" dependency-injection constructor:

public class ThingMaker {
    ...
    public ThingMaker(IThingSource source){
        _source = source;
    }

But then, for classes I am intending as public APIs (classes that other development teams will consume), I can never find a better option than to write a default "bastard" constructor with the most-likely needed dependency:

    public ThingMaker() : this(new DefaultThingSource()) {} 
    ...
}

The obvious drawback here is that this creates a static dependency on DefaultThingSource; ideally, there would be no such dependency, and the consumer would always inject whatever IThingSource they wanted. However, this is too hard to use; consumers want to new up a ThingMaker and get to work making Things, then months later inject something else when the need arises. This leaves just a few options in my opinion:

1. Omit the bastard constructor; force the consumer of ThingMaker to understand IThingSource, understand how ThingMaker interacts with IThingSource, find or write a concrete class, and then inject an instance in their constructor call.
2. Omit the bastard constructor and provide a separate factory, container, or other bootstrapping class/method; somehow make the consumer understand that they don't need to write their own IThingSource; force the consumer of ThingMaker to find and understand the factory or bootstrapper and use it.
3. Keep the bastard constructor, enabling the consumer to "new up" an object and run with it, and coping with the optional static dependency on DefaultThingSource.

Boy, #3 sure seems attractive. Is there another, better option? #1 or #2 just don't seem worth it.