I didn’t think anybody had worse soil that we have here in West Texas. Have you had the soil checked? Ours is a high alkaline soil.
At this point, I'm content to buy garlic at farmers markets. I did drive by a place, in my backroad travels that had a sign *The Garlic Farm*; I'll check them out this spring. ;)
I did learn how to grow great corn at the cg; one year I tried this crazy idea I had; it was like container gardening in a shopping bag. One success from it, was to eliminate weeding. ;)