...it always seems to work this way, doesn't it? I ask the question after hunting through all the docs, then the minute I post I find the answer :)

For anyone looking at this in the future, EditorWindow.OnGUI() appears to only get called when the window is focused. Moving the Repaint() to EditorWindow.OnSelectionChanged() worked.

I've found that adding Repaint() to the Update function of your EditorWindow does the trick. This also has the added effect of repainting the editor window way more often than it does normally which I also found handy in my case.

public void Update()
{
    // This is necessary to make the framerate normal for the editor window.
    Repaint();
}

I suppose if you want your Repaint to be less intrusive you could put it in EditorWindow.OnInspectorUpdate() because it only gets called 10 times per second. That would probably be better for performance.

public void OnInspectorUpdate()
{
    // This will only get called 10 times per second.
    Repaint();
}