This was one case where I'm thinking core aeration makes perfect sense. In fact, I would have done it at double, triple, or even quadruple the normal rate to get the soil to loosen.

You can try 4 oz of shampoo in any amount of water that's convenient, sprayed on the soil. Over time--and you can do that monthly if you're getting normal rainfall or irrigate there--it'll loosen the soil.

How much land are you talking about? If not a lot I think those manual aerators would do the trick and as Morpheus puts it, step up the recommended amount of holes.

Do you find yourself missing the driveway and driving on the grass? If you do that on dry days, it's fine. If you do that on rainy days or when the soil is wet, that's a bad thing and will definitely compact the soil.

Do the shampoo. It's really cheap. It does take 3 full weeks for the screwdriver to go in better. Are you in a hurry to soften this area?