How many professors should I mail in a single university?
This isn't an answer to your question, but the remark that professors might meet over coffee and find out that you emailed a lot of them seemed funny to me. We do meet over coffee and chat. But you have to recognize that (i) we're people too, with families, kids, etc, and when we have coffee, we often have better things to talk about than students emailing us their applications (we might also be talking about actual science, gasp!), (ii) we get a lot of emails from students applying, and the likelihood that we would notice that one of them has emailed a lot of us is very small.