Templated Animation : Can I reference parent properties in a Timeline?

Question

Given the following custom animation class : (From one of the answers to this question) :

public class BrushAnimation : AnimationTimeline {
    public Brush From {
        get { return this.GetValue( FromProperty ) as Brush; }
        set { this.SetValue( FromProperty, value ); }
    }
    public Brush To {
        get { return this.GetValue( ToProperty ) as Brush; }
        set { this.SetValue( ToProperty, value ); }
    }

    public static readonly DependencyProperty
        FromProperty = DependencyProperty.Register(
            "From", typeof( Brush ), typeof( BrushAnimation ) ),
        ToProperty = DependencyProperty.Register(
            "To", typeof( Brush ), typeof( BrushAnimation ) );

    public override Type TargetPropertyType {
        get { return typeof( Brush ); }
    }

    public override object GetCurrentValue(
        object defaultOriginValue,
        object defaultDestinationValue,
        AnimationClock animationClock
     ) {
            return this.GCV(
                defaultOriginValue as Brush,
                defaultDestinationValue as Brush,
                animationClock );
    }

    protected override Freezable CreateInstanceCore( ) {
        return new BrushAnimation( );
    }

    public object GCV(
        Brush defaultOriginValue,
        Brush defaultDestinationValue,
        AnimationClock animationClock
     ) {
        if ( !animationClock.CurrentProgress.HasValue )
            return Brushes.Transparent;

        defaultOriginValue = this.From ?? defaultOriginValue;
        defaultDestinationValue = this.To ?? defaultDestinationValue;

        return animationClock.CurrentProgress.Value == 0 ? defaultOriginValue
            : animationClock.CurrentProgress.Value == 1 ? defaultDestinationValue
            : new VisualBrush( new Border( ) {
                Width = 1,
                Height = 1,
                Background = defaultOriginValue,
                Child = new Border( ) {
                    Background = defaultDestinationValue,
                    Opacity = animationClock.CurrentProgress.Value
                }
            } );
    }
}

Given the following use case :

<ResourceDictionary
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:sys="clr-namespace:System;assembly=mscorlib"
    xmlns:Components="clr-namespace:FooBar.Components"
    xmlns:Animations="clr-namespace:FooBar.Classes">
    <Style TargetType="{x:Type Components:MyButtons}">
        <Setter Property="Template">
            <Setter.Value>
                <ControlTemplate TargetType="{x:Type Button}">
                    <!--Stuff-->
                    <ControlTemplate.Triggers>
                        <EventTrigger RoutedEvent="GotFocus">
                            <BeginStoryboard>
                                <Storyboard>
                                    <Animations:BrushAnimation
                                        Storyboard.TargetName="Foo"
                                        Storyboard.TargetProperty="BarBrush"
                                        Duration="0:0:0.3"
                                        From="<What Do I Put Here?>"
                                        To="<What Do I Put HERE?!>"/>
                                </Storyboard>
                            </BeginStoryboard>
                        </EventTrigger>
                    </ControlTemplate.Triggers>
                </ControlTemplate>
            </Setter.Value>
        </Setter>
    </Style>
</ResourceDictionary>

Based on what I've read, you can't bind a Timelines From and To values because Freezable.

I read a possible workaround but it uses a Tag property and I think this use case may go beyond the scope of that proposed solution.

Is there any way for me to have the Timeline read the values from my component?