Gloria used to do this every night for several weeks when she was an adolescent ham. She was just being a brat, I think she knew I didn't have time to fix it every morning before class and liked getting me frustrated,
lol
Maybe instead of changing cages, just put cardboard aroung the lower bars to prevent her from pushing the bedding out of her current cage. I do this with messy hams, and I weave thin cardboard like from a cereal box in between the bars to deter my hamsters if they go through a bar chewing phase.
Card board is my go to for solving hamster behavioral problems! So versatile and if they chew and destroy it, it's no big deal