It's definitely not too late to be applying for aways. Most programs that I know of don't even start considering visiting students until after their own students have had first choice, and those deadlines tend to be in May/June. Some of the more "competitive" places with fewer spots may have filled, but I'm sure there are a ton of good places out there still, many of whom are very friendly to rotators. Sounds like you may be interested in the South, but I did a rotation at Loyola in Chicago and found them to be very rotator friendly (upside is that it's easy to get a spot, downside is that they get 30-40 rotators per year). Another option is to do a rotation a little later in the fall, since the most popular times are July-September. I already had enough letters, so I did a rotation at a big-name program in November and was one of only 2 rotators at that time. Upside is that you have more one-on-one time to make a good impression and will be the last rotators they see before interviews, downside is that it's too late to get letters usually. Anyway, don't panic because there are a lot of great places to rotate and even if you don't get the exact place you want you can still get one in that geographic region which will still help a lot. Also, it doesn't hurt to call the places that have filled occasionally, because people always cancel their rotations and spots may open up. Good luck!