I booked about this time last year for about the same time as your going this year. As our lord LIL says: you are going to have to cheek out the smaller hotels and guesthouses around PAtong, or look outside at the less popular locations.
Ask if they have a vacency for the first few days you arrive, then at least you have somewhere to stay while you can spend time looking for somewhere more permament.
Check out the phuket-dir for the smaller hotels and guesthouses, although you may have to phone them as alot of the websites listed are not working any more.
If not just try to sleep under the bar at MTB. Ask Nicke to keep a sleeping bag in the cupboard for you. HAve a wash on the beach and take a crap in a beach side restaraunt. You only have to saty awake every night till gone 4am, before you go to bed!
I stayed last year for while at "THe GReen MAnsion" which I booked late, before finding somewhere else. Its listed on here somewhere, so search for it!