I have the same problem side-sleeping in both new and old BF seats. One thing I always bring along now is a standard sized down pillow. In the old BF seats, I place the BF pillow in the L part of the cradle position (the crease?), and use my down pillow for my head. If you are lucky enough to be able to get an extra BF pillow, it helps even more (you can even use a book under the pillow). In the new BF seats, I often will stick a pillow under my ankles in the full "flat" position. I don't know if it really helps with the sliding, but it seems to help me feel more secure in the seat. I often put the BF pillow under my knees or calves when sitting with the legrest up as well. The down pillow is great, it's very light, rolls up pretty small, and fits in my carryon well; plus I have it for my destination (I am a little spoiled by my pillow!) The one I have designated for travel is one of my older ones, cleaned well, but a little less pouffy than a new one, in a colored case so that it doesn't get mixed up with hotel linens..
I feel for you, being a side sleeper is tough on CO aircraft!
Robin