I used a treatment of neem oil, about which I had been somewhat aware, and the leaf spot disappeared almost over night. There are only a few leaves on the tree which still appear infected, and I trimmed these from the tree.
Leaf spot in other areas of the garden seem diminished and reduced, which is (hopefully) sufficient to prevent a spreading disease.
I trimmed away all the diseased roots with pruning shears, and dipped the crown and remaining roots into a solution of hydrogen peroxide (3%).