I know from others how hard it is to find a rental when you have pets.

Have you posted on your local Craigslist, under the Pets section, asking if anyone can suggest a place? I know I see such postings on my CL on a regular basis. Of course, be prepared for the wackos to reply as well, but that may be one source for leads.

Don't be too hard on the friend -- my folks owned rental property and it is all but impossible to make an exception to the rules for one tenant and expect all the others to accept this.

I'm sure you have spoken with people at work to let them know you are looking.

Do you have a shelter near you? Sometimes they will know of places which allow pets -- after all, they won't adopt out to someone who lives where no pets are allowed. I've only just thought of this as I am brain storming for you, not sure if it is a source of leads or not.

I'm sure this is stressful, having a deadline and no place to go as yet. I'm also sure something WILL develop for you. Keep searching!