How to select all the text when the edit textbox in a DataGridTemplateColumn receives focus ?

Question

I'm trying to get a DataGridTemplateColumn to behave identically to a TextColumn

• when the cell goes into edit mode (Press F2), the user can immediately start typing in the new value
• by default, existing text content is selected - so that you can set new values easily

Got the first one done ; however selecting all the text isn't working. As mentioned by a number of posts, tried hooking into the GotFocus event and selecting all the text in code-behind. This worked for a standalone textbox ; however for a Textbox which is the edit control for a TemplateColumn, this doesn't work.

Any ideas? Code Sample:

<Window.Resources>
            <Style x:Key="HighlightTextBoxStyle" TargetType="{x:Type TextBox}">
                <EventSetter Event="GotFocus" Handler="SelectAllText"/>
                <EventSetter Event="GotMouseCapture" Handler="SelectAllText"/>
                <Setter Property="Background" Value="AliceBlue"/>
            </Style>

            <DataTemplate x:Key="DefaultTitleTemplate">
                <TextBlock Text="{Binding Title}"/>
            </DataTemplate>
            <DataTemplate x:Key="EditTitleTemplate">
                    <TextBox x:Name="Fox"
                         FocusManager.FocusedElement="{Binding RelativeSource={RelativeSource Self}}"  
                         Text="{Binding Path=Title, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}"
                         Style="{StaticResource HighlightTextBoxStyle}">
                    </TextBox>
            </DataTemplate>
        </Window.Resources>
        <DockPanel>
            <TextBox DockPanel.Dock="Top" x:Name="Test" Text="{Binding Path=(FocusManager.FocusedElement).Name, ElementName=MyWindow}" 
                     Style="{StaticResource HighlightTextBoxStyle}"/>
            <toolkit:DataGrid ItemsSource="{Binding Items}" AutoGenerateColumns="False">
                <toolkit:DataGrid.Columns>
                    <toolkit:DataGridTemplateColumn Header="Templated Title" 
                        CellTemplate="{StaticResource DefaultTitleTemplate}"
                        CellEditingTemplate="{StaticResource EditTitleTemplate}" />

                    <toolkit:DataGridTextColumn Header="Title" Binding="{Binding Path=Title}" />
                </toolkit:DataGrid.Columns>
            </toolkit:DataGrid>
        </DockPanel>