I saw a recipe once for hardened clay floors. Basically the guy dug up the top 6-8" and screened it through 1/4" screen, then added rock salt (although I imagine ice melt would work). Don't remember how much he added. But then he very lightly moistened the clay and put it back, tamped it in, and I guess it is pretty darn hard now. Once the salt is in the floor, I don't know if it would affect steel in the vicinity or not.
On the other hand, you could treat it like rammed earth walls. Dig out the top foot. Mix up some sharp sand and small (preferably sharp crusher material) gravel with your clay, moisten slightly run a hand rammer or jumping jack over it in 3" or so lifts. Once you are up to level and very solid, let it dry about a week or two in dry weather, then spray it down with boiled linseed oil. First time, straight. Next time, 1/3 mineral spirits by volume, then once mixed half and half. Should be harder than XXXXX, fairly waterproof and sweepable.