What is the quickest way to get the background color of a single character in a RichTextBox?

Question

Using WinForms, I have a RichTextBox which will hold the contents of a text file whose length will be limited only by what a RichTextBox can manage.

A section within it will be marked using a certain background color. I need to quickly identify where the section begins and ends. I don't trust that the section will be completely unbroken, and the marked area might cover the entire text--so I need to examine the background color of every character.

The obvious way to do this is to select each character in turn and get its SelectionBackColor:

  private TextRange? CalcMarkedTextRange() {

    var rtb = RichTextBox;
    var textLength = rtb.TextLength;

    // Store the range of whatever the user currently has selected

    var currentSelectionRange = new TextRange( rtb );

    rtb.Visible = false; // <--- To prevent slow screen updates

    // Find where the first and last color-marked characters are

    var markBegins = -1;
    var markEnds = -1;

    for ( int ix = 0; ix < textLength; ++ix ) {
      rtb.Select( ix, 1 );
      if ( rtb.SelectionBackColor == SelectedTextBackColor ) {
        if ( markBegins == -1 ) {
          markBegins = ix;
        }
        markEnds = ix;
      }
    }

    // Put back user's selection

    rtb.Select( currentSelectionRange );

    rtb.Visible = true;

    // See what we found

    if ( markBegins > -1 ) {
      // Return a single range encompassing all marked characters
      return new TextRange( markBegins, markEnds - markBegins + 1 );
    }

    return null;

  }

In the code above, TextRange is a structure that stores the start and length of a selection, just as you might expect.

If I don't hide the control by messing with its Visible property before scanning the colors, this code is unbelievably slow. You can see it scanning through, even with a relatively small amount of text. My test using about 4000 characters exhibited unacceptably poor performance.

I do hide it, it operates much more quickly, but there is still an ugly flash as the control disappears for a few seconds then comes back with its scroll position slightly off.

There must be a way to know the background color of an individual character without having to select it, though I imagine one would have to call a native Win32 method. But I have had no luck finding one.