I have the same problem with concrete. Tillers don't stand a chance. Meadow creature broadfork loosend it up till summer rains packed it back down. My main kitchen garden took 3 years to be able to properly grow good veg. I had to add about 2 ft. of hay every fall to rot down, added 1000s of earthworms and grew lots of dikon radish's and left to rot in ground. ( those things really drill through hard-pan and clay). Finally I can dig down 8-10 inches with my hands alone. Its been many years. Still add a foot or two of hay to rot down every fall. just part the hay where I want rows,shove broadfork deep down and wiggle it, add a little compost on top for seeds, or just set starts in the earth. Years of rotting hay has made the difference.