Sorry, I have no advice, but I'm in the same boat. Except, I am trying to fill 36 full time spots in a daycare centre.
As for the week free: I wouldn't offer something for free, I would offer something the other places don't. For example: Monthly progress reports, a menu that has been approved by a dietician (often colleges or university students studying nutriton will do this for free). Perhaps, a speciailized music program, reading cards....etc (you can order a lot of educational packages online) and you could call the newspaper and have them do an editorial on the new program being offered in your dayhome. Newspapers don't charge for an editorial, most of the time, it doesn't hurt to make a few phone calls to the television, radio etc....the worst they can say is 'no' if you ask for a free interview.
Good luck! Good things come to those who wait.....right?

ETA: spelling.