Would it be possible to make a fake edit box, which isn't actually an edit box. By that I mean have the real edit box but hidden somewhere, then once you give focus to the fake edit box, it's actually giving focus to the real and hidden edit box. Then have the fake one output whatever is written in the real edit box. That way the fake one would sit nicely under your custom cursor while the offending real one will be hidden and not getting in the way, but you'll still be basically using it, which if anything else in your game NEEDS the real thing available to work correctly, will continue to work correctly.
There's probably a far easier way of solving it than that, but I haven't had my morning coffee yet