Apply base style of window to inherited window - wpf

Question

I have defined a style for the Window class in my ResourceDictionary:
<Style x:Key="windowStyle"
TargetType="{x:Type Window}">
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type Window}">
<Border Width="300" Height="300" BorderBrush="Red" BorderThickness="3">
<ContentPresenter />
</Border>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
Now I want a specialized window. To this end I inherit a new class from Window and add custom DependecyProperties etc.
My goal is to reuse the base style, ie. I pretty much only want to fill the ContentPresenter from the base style with a grid and add a new ContentPresenter in one of its cells, so I tried this:
<Style x:Key="customWindowStyle"
BasedOn="{StaticResource windowStyle}"
TargetType="{x:Type local:CustomWindow}">
<Setter Property="ContentTemplate">
<Setter.Value>
<ControlTemplate TargetType="{x:Type local:CustomWindow}">
<Grid>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="Auto" />
<ColumnDefinition Width="*" />
</Grid.ColumnDefinitions>
<Image Grid.Column="0" Source="{TemplateBinding Source}" />
<ContentPresenter Grid.Column="1" />
</Grid>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
Which gives me an exception at runtime, since the ContentTemplate is of type DataTemplate as opposed to ControlTemplate. Of course if I Set the Template instead of ContentTemplate in the customWindowStyle, I lose the style of the base window.
Is there another way to achieve this goal?