The answer is to not use a UserControl to do it.

Create a class that extends ContentControl

public class MyFunkyControl : ContentControl
{
    public static readonly DependencyProperty HeadingProperty =
        DependencyProperty.Register("Heading", typeof(string),
        typeof(HeadingContainer), new PropertyMetadata(HeadingChanged));

    private static void HeadingChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
    {
        ((HeadingContainer) d).Heading = e.NewValue as string;
    }

    public string Heading { get; set; }
}

then use a style to specify the contents

<Style TargetType="control:MyFunkyControl">
    <Setter Property="Template">
        <Setter.Value>
            <ControlTemplate TargetType="control:MyFunkyContainer">
                <Grid>
                    <ContentControl Content="{TemplateBinding Content}"/>
                </Grid>
            </ControlTemplate>
        </Setter.Value>
    </Setter>
</Style>

and finally - use it

<control:MyFunkyControl Heading="Some heading!">            
    <Label Name="WithAName">Some cool content</Label>
</control:MyFunkyControl>