This pathogen favors acidic soil conditions (http://www.ncbi.nlm.nih.gov/pubmed/15077673), therefore any fertilizers that make the substrate more alkaline will suppress the pathogen's virulence and maintain conditions where the plants are more likely to defend themselves. Since many water soluble fertilizers are acidic, they can lower the pH of the substrate and allow fungi like S. sclerotium to thrive. Adding limestone to the soil/substrate can help, otherwise find water soluble fertilizers that contribute to alkalinity.
In that case, making raised beds (even higher than normal) may give you the drainage/drying advantage that will help stop the pathogen from spreading. You may also add charcoal or expanded clay beads to provide more air-filled pore space to the clay soil. I do not want to suggest chemical control until everything else is attempted. Best of luck with your research!