My 10x12 shed floor heaved an inch after the first hard freeze in Boise

Poured a concrete pad for a 10x12 shed back in August and felt pretty good about it. First real cold snap hit Boise in early November and the slab heaved up close to an inch on the north corner. Turns out I skipped a proper gravel base and the dirt under it held water like a sponge, then froze and pushed everything up. The shed door now drags on the frame so bad I have to shoulder it open, and the whole thing rocks when I walk to the back. I'm looking at tearing out that corner and redoing it with 6 inches of compacted 3/4 crush and a French drain running away from the slab. Has anyone fixed a heaved slab without tearing the whole thing out, or am I just wasting my time and should rip it all up?