Set the price high and gauge their reaction dosen't sound like you're pitching up against anyone else so all they can say is "HOW MUCH!" and you come to a compramise.
I went in with a mad price for a job a while back because I wasn't to keen on working with the company but I still wanted to show willing. So i well over cost the job and they looked at the propasal and just signed it off with a big YES!