I concur with Alex, hay or straw, either one will provide what that clay needs to become good soil. To either of these "covers" you will want to pour on fungal slurries (whizzed up
mushroom caps from anywhere) and when you have it ready compost teas.
By making the additions of compost teas and mushroom slurries you are adding microbiome organisms and those will do the work of turning the medium (the hay or straw) into soil nutrients by being eaten by the good microbiome you are adding.
When using hay or straw, deeper is better, I use full, rectangular bales of straw, these measure around 4' long, 24" wide, and 28" tall. If you use full rectangular bales stand them open ends (of the individual straws) up so liquids can pass through the straws.
Good luck
Redhawk