I was in Cabarete on Wednesday this week and I was looking at all the rooms advertised at Janet's supermarket, on the boards on the wall outside. Take your pick for between RD$ 8000 and RD$ 10000 per month. I agree with the other comments, the best thing is to go to Cabarete, rent a room for a week somewhere and then look around for something long-term. Everything you will see advertised online is likely to be just for tourists. It's also very important that you see the place you are going to rent before you sign up. And if you get the chance, try staying there a couple of nights. There are a lot of very noisy bars and discos in Cabarete and some parts can be quite dangerous.
I also suspect that nobody has really got their act together properly for January, so when you are seeing "no vacancy" it's just that they haven't got prices or haven't loaded their availability. Things in this country are pretty disorganised at the best of times.