I'm not sure about suggestions for mitigating the leak during the winter while you wait, but we did a removal and replacement (same window, just cleaned it up and re-seated it) of our rear window last spring. Before removing it we tried recaulking it around the edge and that seemed to help, but it still leaked. Here's a link to our blog detailing what we did:
Rear WindowHOWEVER, ultimately we think that the rear cyclops might have been our biggest culprit. Shortly after the window replacement (before the next hard rain) one of our bulbs burned out and in taking it off we realized it was all moldy and corroded in there, and that it wasn't sealed well at all. It sure seemed like a big leak point. So we replaced that as well. We are bone dry now, so we're not 100% sure which one it was, or perhaps a combination of the two.