If you are lucky you may be OK.
If you try at high season 20th December to 10th Jan then they are fully booked now.
Always one to keep in mind.
There are also a lot of these units at Patong Tower rented privately. Try seaching the Gazette or place your own add one month before you plan to travel.
Oh one more I also forgot about is The place to Stay, which I have had a look at but never stayed in.
There is also the Yorkshire Inn which has an aprtment and its at the end of the nighlife area in Soi Sansabi
The Place To Stay - Phuket, Thailand
Luxury Apartments in Patong, Phuket, Thailand near soi Bangla
Regards
Drew