Many years back when I bought my present home, I had a similar problem.
The soil was terrible. Back then, I had access to rice hulls - a
bi-product of the rice growing industry, here in the Sacramento area.
They were very cheap, and light. I mixed them into the soil, and
instantly noticed how they made the soil so much easier to work, and to
weed. Things would actually grow in the garden, because bulbs and
seeds weren't becoming entombed in the clay.
I don't know if you have rice hulls available in your area. . .but it's
something you might want to investigate.