Have you tried a scarf (a la "I Love Lucy")?
My hair isn't as short as yours, but since my cut I've had to adjust my sleep method. I use mix of clips and short pineapples, all high enough on my head so that it doesn't hurt. I'm not sure your hair is long enough to do it though.
You should check out xcptnl thread about the night of many experiments. She said sleeping pre-scrunching was promising. She also has shorter hair.
The Night of many Experiments