If she'll take rabbits then keep her on them, one every 3-4 weeks with exercise should slowly melt the fat off of her.
Remember to feed rabbits based on their weight rather than having the prey be the thickness of the snake. As you noted rabbit is a very lean meal, with minimal fat, lots of muscle, and larger bones than rats. So, a rabbit with the same girth as a rat can weigh a good bit more because muscle and bone are more dense than fat.
I feed rabbits to my boas (BCI's, BRB's, and Dum's), and my supplier has rabbit kits that my king snakes and adult savu python love.