How to use the Binding DataGridTextColumn inside CellStyle, ElementStyle and EditingElementStyle in WPF

I would like to modify the Template of the CellStyle, ElementStyle and EditingElementStyle of the DataGridTextColumn (and also DataGridComboBox and DataGridTemplateColumn later on).

Let's say I have the following column:

<DataGridTextColumn
    CellStyle="{StaticResource DataGridTextColumnCellStyle}"
    ElementStyle="{StaticResource DataGridTextColumnElementStyle}"
    EditingElementStyle="{StaticResource MyPropertyataGridTextColumnEditingElementStyle}"
    Header="My Property">

    <DataGridTextColumn.Binding>

        <Binding
            Mode="TwoWay"
            NotifyOnValidationError="True"
            Path="MyProperty"
            UpdateSourceTrigger="PropertyChanged"
            ValidatesOnDataErrors="True"
            ValidatesOnNotifyDataErrors="True">

            <Binding.ValidationRules>

                <vr:MyPropertyValidationRule ValidationStep="RawProposedValue" />

            </Binding.ValidationRules>

        </Binding>

    </DataGridTextColumn.Binding>

</DataGridTextColumn>

I don't really know what is the difference btw. CellStyle and ElementStyle, but I would rather consider the EditingStyle here. Note that I've prefixed the the key name with MyProperty because I don't know yet how to "reuse" the binding of the DataGridTextColumn inside the Template of the EditingElementStyle.

<Style x:Key="MyPropertyDataGridTextColumnEditingElementStyle" TargetType="{x:Type TextBox}">

    <Setter Property="Template">
        <Setter.Value>
            <ControlTemplate>

                <!--  CustomTextBox is a UserControl that contains some styling, in particular with the validation error  -->
                <!-- (probably a bit overkill, but I have similar other UserControl for ComboBox, DatePicker, etc.  -->
                <controls:CustomTextBox Color="{TemplateBinding Foreground}">

                    <!--  How to avoid rewriting all the binding here are "reuse" the one written in the DataGridTextColumn?  -->
                    <!--  Otherwise, I'm afraid that I will have lots of dupplicated styles for each column  -->
                    <Binding
                        Mode="TwoWay"
                        NotifyOnValidationError="True"
                        Path="MyProperty"
                        UpdateSourceTrigger="PropertyChanged"
                        ValidatesOnDataErrors="True"
                        ValidatesOnNotifyDataErrors="True">

                        <Binding.ValidationRules>

                            <vr:MyPropertyValidationRule ValidationStep="RawProposedValue" />

                        </Binding.ValidationRules>

                    </Binding>

                </controls:CustomTextBox2>

            </ControlTemplate>
        </Setter.Value>
    </Setter>

</Style>

I tried to directly bind the Text property of the CustomTextBox with RelativeSource to the DataGridColumn, but I get errors such as "A two-way binding requires a Path or XPath".

I'm sure that I'm missing something.