How to bind to a singleton property in Silverlight 4?

Hi all first post here :) Let's start with a snippet of the code I'm using:

public MyClass : INotifyPropertyChanged
{
  private static MyClass _instance;
  public static MyClass Instance
  {
      get
      {
          if (_instance == null)
              _instance = new MyClass();
          return _instance;
      }
  }

  private bool _myProperty;
  public bool MyProperty
  {
      get
      {
        return _myProperty;
      }
      set
      {
          if (_myProperty!= value)
          {
              _myProperty= value;
              NotifyPropertyChanged("MyProperty");
          }
      }
   }

   private MyClass() { ... }
}

As you can see, it's a singleton class. In my view, I want to bind a control on MyProperty. My initial idea was to import MyClass as a static ressource in my view using something like:

<UserControl x:Class="Metrics.Silverlight.ChartView"
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
  xmlns:logic="clr-namespace:Metrics.Logic;assembly=Metrics.Logic">
  <UserControl.Resources>
    <logic:MyClass x:Key="myClass" />
  </UserControl.Resources>
</UserControl>

And bind it like so:

<Button Margin="5" Click="btnName_Click"  Visibility="{Binding Source={StaticResource myClass}, Converter={StaticResource visibilityConverter}, Path=MyAttribute, Mode=OneWay}">

Of course, this approach won't work since MyClass constructor's is private. I also cannot use x:static since it's not available in Silverlight 4.

I've been stuck on this problem far longer than I should have... How can I bind on MyProperty?

Any ideas?

Thanks in advance!