4 of our 10 Disney Cruises have been on points & we have always called member services. You could check the DCL website to get an idea of what cabins might be available. You can also look at cruisefish.com.
I recently booked for spring break on points, and have 4 or 5 different picked out as options. From 4/18 -4/29. all 3 or 4 day. All had availability. Some only has a bit higher points options, but was very happy with availability and this was for Spring break. I bet you will be pleasantly surprised.