Dear LS,
Each to his own! It's so tempting to find just that little bit more ...
Ramadan means that there will be slower service than usual in the daytime, and that you may not be served alcoholic beverages (at worst!). Things will be very lively at night, when Muslims can eat and drink freely (they fast during the hours of daylight), but you might find some of the shops closed. I would strongly advise you to contact the Moroccan Tourist Office in London and ask their advice. They will be able to give you a more up-to-date point of view, and if you ask what happens as regards hotels, you should have more help!
As for the 'cheap' and authentic Riads - I can't really advise, because although the authenticity is certainly appealing, I can't help thinking that as regards hygiene, a cheap hotel or Riad may not be in your best interests. Have you considered pre-booking a week and then finding somewhere for your second week once actually there? You could also see if you could book another week at the hotel you're already at if you don't find something suitable ... but it may cost more 'on the spot' than pre-booked.
You could also contact a good tour agency (Atlas Tours who handle all of Marmara's FIT) to see if they could suggest some and perhaps even book on your behalf.
Do make sure your jabs are up to date though!