I suffer from insomnia when on Prednisone, the last blast I had of it @60 mgs, I would easily stay up for 2 days straight. It was kind of funny that last time too, the GI was surprised and I asked him, "you really weren't aware it could affect someone like that?" I chuckle to myself knowing I've had the disease longer than he's been alive.
As Habs said, sounds like you're doing the right things. I do the same, exercise early in the AM, meditate before going to bed and read in bed. If I do manage to sleep, it's brief, 3 to 4 hours.
Taking the Prednisone I already know the drill and how it's going to affect me, I bear with it for those few weeks the best I can and once at the lower end of the taper, I manage to sleep.