I guess I did the opposite of "jinxing" myself. When I called CIC again, I was able to get through to a representative by phone. I asked my questions, and then I asked her about your police certificate issue. She said if it is older than three months, even if it was issued after you submitted your application, it is no longer valid. You will need to request another.
She was a little bit confusing. I didn't do my medical or police certificate with my application. I asked if I could go ahead and do that now, instead of waiting for CIC to request them from me, so that I wouldn't cause any unnecessary delays in processing. She advised me to wait until CIC requested the documents. However, she said that waiting for me to send them could cause additional delays. She said, "I can only advise you to wait until the documents are requested. However, I know that some people have sent them in before the request. You can certainly do that." So...I don't really know whether you should wait for the request or just get another certificate and send it along.
She did confirm that I should send the documents to the same office where I sent my original application (Vegreville, for me).
Hope that helps!