Force constant refreshing of WINE window
I've found a completely horrendous but workable way of fixing my problem. First, download and install Afloat, which lets you set windows as global translucent non-clickable overlays.

Then, create a HTML file whose background switches between pure white and almost pure white 20 times a second. Something like this:

&lt;!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"&gt;
&lt;html xmlns="http://www.w3.org/1999/xhtml"&gt;
  &lt;head&gt;
    &lt;meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" /&gt;
    &lt;title&gt;Strobe Light&lt;/title&gt;
    &lt;script language="javascript" type="text/javascript"&gt;
      &lt;!--
      var c = 0;

      function strobe() {
        document.bgColor = c ? '#fefefe' : '#ffffff';
        c = (c + 1) % 2;
      }

      function startStrobe() {
        setInterval(strobe, 50);
      }
      --&gt;
    &lt;/script&gt;
  &lt;/head&gt;
  &lt;body onload="startStrobe();"&gt;
  &lt;/body&gt;
&lt;/html&gt;


Finally, open this file in Safari, resize the window to fill the screen as much as possible, and use Afloat to set the window as a global near-transparent non-clickable overlay. The result? The whole screen (including the WINE window) is forced to update every 50 ms.

Is this completely horrible? Yes. But it works.