WPF Dynamic Layout with ItemsControl and Grid

I am creating a WPF form. One of the requirements is that it have a sector-based layout so that a control can be explicitly placed in one of the sectors/cells.

I have created a tic-tac-toe example below to convey my problem:

There are two types and one base type:

public class XMoveViewModel : MoveViewModel
{
}
public class OMoveViewModel : MoveViewModel
{
}
public class MoveViewModel
{
    public int Row { get; set; }
    public int Column { get; set; }
}

The DataContext of the form is set to an instance of:

public class MainViewModel : ViewModelBase
{
    public MainViewModel()
    {
        Moves = new ObservableCollection<MoveViewModel>()
        {
            new XMoveViewModel() { Row = 0, Column = 0 },
            new OMoveViewModel() { Row = 1, Column = 0 },
            new XMoveViewModel() { Row = 1, Column = 1 },
            new OMoveViewModel() { Row = 0, Column = 2 },
            new XMoveViewModel() { Row = 2, Column = 2}
        };
    }
    public ObservableCollection<MoveViewModel> Moves
    {
        get;
        set;
    }
}

And finally, the XAML looks like this:

 <Window.Resources>
    <DataTemplate DataType="{x:Type vm:XMoveViewModel}">
        <Image Source="XMove.png" Grid.Row="{Binding Path=Row}" Grid.Column="{Binding Path=Column}" Stretch="None" />
    </DataTemplate>
    <DataTemplate DataType="{x:Type vm:OMoveViewModel}">
        <Image Source="OMove.png" Grid.Row="{Binding Path=Row}" Grid.Column="{Binding Path=Column}" Stretch="None" />
    </DataTemplate>
</Window.Resources>
<Grid>
    <ItemsControl ItemsSource="{Binding Path=Moves}">
        <ItemsControl.ItemsPanel>
            <ItemsPanelTemplate>
                <Grid ShowGridLines="True">
                    <Grid.RowDefinitions>
                        <RowDefinition />