It sounds like you are discovering those things that you never think about, and nobody remembers to talk about. Dirt is a funny thing, and it sure does behave differently depending on how much water it has. I try to spread it out with every load to the best of my ability, but to also keep on moving as quickly as possible. The inital loads will all become covered quickly enough, so it's the in final finish that I'm thinking about. When I start getting close to that,I really slow down and spend more time on it.
If the dirt is too hard to mess with after it dries out, I'd probably leave it alone for now. Rain will come again and soften it up for you. It's just a matter of timing when you can get back at it and how quickly it hardens up on you again.
I've also found that there is a crust on clay when it hardens, but once you break it, the soil below that crust is soft and very managable. I've had issues with breaking the crust or shell on clay with my 40,000 pound dozer!!!
Keep at it, we're enjoying your progress.
Eddie