Multiple functions to establish a fallback value for a property until not null

I have a property (called "Head") that can be set externally. When "Head" is not set, it uses Unity3D's MonoBehaviour functions to try to find the best value for "Head". I started with a nested if, but the nesting was starting to get out of hand.

if (Head == null)
{
    Head = this.GetComponent<Camera>();

    if (Head == null)
    {
        Head = this.GetComponentInChildren<Camera>();

        if (Head == null)
        {
            Head = Camera.main;
        }
    }
}

So I developed a loop:

System.Func<Camera>[] fallbacks = new System.Func<Camera>[]
{
    () => this.GetComponent<Camera>(),
    () => this.GetComponentInChildren<Camera>(),
    () => Camera.main,
};

foreach (var fallback in fallbacks)
{
    if (Head != null)
    {
        break;
    }
    Head = fallback();
}

Would this create too much lambda overhead? Do you think the lambdas even increases readability? Is there a more elegant way to handle multiple fallbacks?

Edit:

RobH helped me discover the Null coalescing doesn't work with Unity3D components. RobH's extension method workaround worked great with some tweaking. I had to enforce that comparison had to be done through UnityEngine.Object.

public static T IfNullThen<T>(this T obj, Func<T> factory) where T : UnityEngine.Object
{
    return obj != null ? obj : factory();
}

With that extension method my code is now just

Head = Head
    .IfNullThen(() => this.GetComponent<Camera>())
    .IfNullThen(() => this.GetComponentInChildren<Camera>())
    .IfNullThen(() => Camera.main);