DataGridTemplateColumn (ComboBox, DatePicker) Resets/Clears and doesn't fire AddingNewItem

I've narrowed down the problem to the following example that has a DataGrid with three columns.

If the first column you click on in the new item row is 'DateWorks' or 'Text', then you will raise the AddingNewItem event.

If instead you click the 'DateDoesntWork' column first, you can select a date, but no new item is added until you move to one of the other columns, at which point the value in the 'DateDoesntWork' DatePicker gets cleared.

What on earth is going on?

XAML:

<Window x:Class="DataGridColumnTemplate_NotFiringAddingNewItem.MainWindow"
        xmlns="http://ift.tt/o66D3f"
        xmlns:x="http://ift.tt/mPTqtT"
        Title="MainWindow" Height="350" Width="525">
    <Grid>
        <DataGrid x:Name="dg" HorizontalAlignment="Left" Margin="10,10,0,0" VerticalAlignment="Top" Height="299" AutoGenerateColumns="False" Width="497" AddingNewItem="dg_AddingNewItem" CanUserAddRows="True">
            <DataGrid.Columns>
                <DataGridTemplateColumn Header="DateWorks">
                    <DataGridTemplateColumn.CellEditingTemplate>
                        <DataTemplate>
                            <DatePicker SelectedDate="{Binding InvoiceDate}" />
                        </DataTemplate>
                    </DataGridTemplateColumn.CellEditingTemplate>
                </DataGridTemplateColumn>
                <DataGridTemplateColumn Header="DateDoesn'tWork">
                    <DataGridTemplateColumn.CellTemplate>
                        <DataTemplate>
                            <DatePicker SelectedDate="{Binding InvoiceDate}" />
                        </DataTemplate>
                    </DataGridTemplateColumn.CellTemplate>
                    <DataGridTemplateColumn.CellEditingTemplate>
                        <DataTemplate>
                            <DatePicker SelectedDate="{Binding InvoiceDate}" />
                        </DataTemplate>
                    </DataGridTemplateColumn.CellEditingTemplate>
                </DataGridTemplateColumn>
                <DataGridTextColumn Header="Text" Binding="{Binding Description}"/>
            </DataGrid.Columns>
        </DataGrid>
    </Grid>
</Window>

C#:

public partial class MainWindow : Window
{
    public MainWindow()
    {
        InitializeComponent();

        List<JobCostEntity> l = new List<JobCostEntity>()
        { 
            new JobCostEntity() { Id = 0, InvoiceDate = DateTime.Now, Description = "A"},
            new JobCostEntity() { Id = 0, InvoiceDate = DateTime.Now, Description = "B"}
        };

        dg.ItemsSource = l;
    }
    private void dg_AddingNewItem(object sender, AddingNewItemEventArgs e)
    {
        MessageBox.Show("AddingNewItem");
    }
}

public partial class JobCostEntity
{
    public int Id { get; set; }
    public int JobId { get; set; }
    public Nullable<int> JobItemId { get; set; }
    public Nullable<System.DateTime> InvoiceDate { get; set; }
    public Nullable<System.DateTime> ProcessedDate { get; set; }
    public int PackageId { get; set; }
    public int DelegateId { get; set; }
    public string Description { get; set; }
    public Nullable<decimal> LabourCost { get; set; }
    public Nullable<decimal> PlantOrMaterialCost { get; set; }
    public Nullable<decimal> SubcontractorCost { get; set; }
    public Nullable<decimal> TotalCost { get; set; }
    public bool Paid { get; set; }
}

It's arguably(!) desirable to have the DatePicker already visible to the user (hence both a CellTemplate and a CellEditingTemplate), rather than them have to click the cell to 'reveal' the control.

Is there some way I have to inform the DataGrid that my DataGridTemplateColumn Control has just set a value on a new row? If so, how so?!