Hi JoyLynn -
Part of the issue with our clay is that it is a sloppy mess much of the year, because it rains here from October to May. Working with it when it is wet is not wise because it gets compacted. Then in the summer, we get no rain and the clay gets hard as a rock. Another issue we have is that anywhere the ground has been exposed to the weather for a long time (like all the grassy areas in the sun where you'd want the plant a vegetable garden), the clay has turned into hardpan which is pretty much like rock. Sometimes you can break it up with a pickax, but usually that's a futile effort.
I've found a couple solutions to the issue that have made gardening much easier here. The soil gets a lot better after it's heavily mulched with arborist chips for a few years. Sounds kind of like what you are doing. We've been doing that for about 5 years now, and the soil is much more workable. And when planting something in an area with hardpan, we just pile up 6 to 8" of soil on the top of the area and put in the plant. Everything I've done this with is doing just fine. For the garden beds, we have made raised beds, but we also kind of hugelkultured in them by adding cardboard, putting branches and leaves on that, then adding soil and compost. With both these methods, we don't even have to dig up the grass, so easy-peasy!
Does your clay not turn into hardpan ever? Maybe it's all the rain we get that pounds the clay into brick.....