How to set a TypeConverter on an attached dependency property in Silverlight?

My goal is to be able to write this in XAML:

<Grid>
    <Rectangle Fill="AliceBlue"
            myCore:MyTimePanel.BeginningDate="03/03/2010"
            />
</Grid>

Problem : Silverlight XAML can't parse a DateTime from a string. So at runtime I have the XamlParseException "can't create a DateTime from that string".

When I use a simple DependencyProperty, I simply add a TypeConverterAttribute on the getter/setter and it works. Like this (idea from here):

[TypeConverter(typeof(DateTimeTypeConverter))]
public DateTime MyDate
{
    get { return (DateTime)GetValue(MyDateProperty); }
    set { SetValue(MyDateProperty, value); }
}

But with an attached DP, there is no getter/setter. What can I do to be able to write the string date in XAML ?

Thanks !