Well over the weekend we may have found a place to stay in the centre of Florence for the wonderful price of 750euros per month.  It is a 2/3 bedroom apartment with 2 bathrooms and fully furnished.  For all you Aussies this equates to approx. $285 per week. 
I am just waiting on my italian friend to let me know what she thinks of it and the landlady.  If all is good then I am booking it.  I do not want to miss out on such a great apartment.
If you persist you will find people in Italy who would rather have a long term renter than a short term holiday rent.
When I have secured it I will post some photos.