VisualBrush を使用してキャンバスにバインドすることで、質問に対する答えを見つけたようです。
<Canvas Name="backgroundCanvas" Visibility="Visible" Height="{StaticResource animHeight}" Width="6144">
<Canvas Name="menuFrontCanvas" Visibility="Visible" Margin="0,0,0,0" Height="{StaticResource animHeight}" Width="{StaticResource animWidth}">
<Rectangle HorizontalAlignment="Left" VerticalAlignment="Top" Width="{StaticResource animWidth}" Height="{StaticResource animHeight}">
<Rectangle.Fill>
<VisualBrush Visual="{Binding ElementName=menu4Canvas}" />
</Rectangle.Fill>
</Rectangle>
</Canvas>
<Canvas Name="menu1Canvas" Visibility="Visible" Margin="1024,0,0,0" Height="{StaticResource animHeight}" Width="{StaticResource animWidth}">
<Image Name="alpsLogoImage" Canvas.ZIndex="99" Stretch="None" HorizontalAlignment="Left" VerticalAlignment="Top" Visibility="Visible"
IsEnabled="True" StretchDirection="Both" Source="WPFResources/ALPSLogo.png" />
<Image Name="menu1Image" Stretch="None" HorizontalAlignment="Left" VerticalAlignment="Top"
IsEnabled="True" StretchDirection="Both" Source="WPFResources/Backgrounds/menu1Image.png" />
</Canvas>
<Canvas Name="menu2Canvas" Visibility="Visible" Margin="2048,0,0,0" Height="{StaticResource animHeight}" Width="{StaticResource animWidth}">
<Image Name="menu2Image" Stretch="None" HorizontalAlignment="Left" VerticalAlignment="Top"
IsEnabled="True" StretchDirection="Both" Source="WPFResources/Backgrounds/menu2Image.png" />
</Canvas>
<Canvas Name="menu3Canvas" Visibility="Visible" Margin="3072,0,0,0" Height="{StaticResource animHeight}" Width="{StaticResource animWidth}">
<Image Name="menu3Image" Stretch="None" HorizontalAlignment="Left" VerticalAlignment="Top"
IsEnabled="True" StretchDirection="Both" Source="WPFResources/Backgrounds/menu3Image.png" />
</Canvas>
<Canvas Name="menu4Canvas" Visibility="Visible" Margin="4096,0,0,0" Height="{StaticResource animHeight}" Width="{StaticResource animWidth}">
<Image Name="menu4Image" Stretch="None" HorizontalAlignment="Left" VerticalAlignment="Top"
IsEnabled="True" StretchDirection="Both" Source="WPFResources/Backgrounds/menu4Image.png" />
</Canvas>
<Canvas Name="menuBackCanvas" Visibility="Visible" Margin="5120,0,0,0" Height="{StaticResource animHeight}" Width="{StaticResource animWidth}">
<Rectangle HorizontalAlignment="Left" VerticalAlignment="Top" Width="{StaticResource animWidth}" Height="{StaticResource animHeight}">
<Rectangle.Fill>
<VisualBrush Visual="{Binding ElementName=menu1Canvas}" />
</Rectangle.Fill>
</Rectangle>
</Canvas>
</Canvas>