How to Improve clay soil by next season

Next year i would like to grow corn in a patch of ground which had weeds/lawn but was not very well maintained. I have mowed it on the lowest setting and added all my lawn mower clippings on top then covered it with weed mat.

My plan is to leave the weed mat on for a month then get rid of what is left by hand. Then Till/Shovel it around. Adding Some blood and bone and gypsum.

After That the plan is to grow some Long White Chinese Radish because I don't have any Daikon seed. when harvesting put the leaves on top of the ground. Then putting in some broad beans as a green Manure. Cutting them at stem and adding the leaves to the top at the start of the season.

I am in Canberra, Australia. I would like to spend very little money but have plenty of time. Happy to Give more information if needed.