I feel solarization doesn't work as well as it seems it ought to. Does that sentence make sense? It works best at the surface and the great heat sink of the ground makes the heat effects diminish rapidly with depth. I suspect you'll have to turn the "infected" layers often and get seriously vicious with it for it to work.

So, even with that, you won't have compost (or anything else) remain sterile for long if it's outdoors sitting in the dirt!

When properly done solarizing soil will get the top 6 inches of soil to about 140 degrees, hot enough to kill off many soil borne disease pathogens. Since these pathogens are killed off it only stands to reason that beneficial organism would also be killed off since they do tend to be less hardy then the disease pathogens.
Potatoes, members of the nightshade family, do well but other members of that family do not may indicate the source of the diseases might not be the soil. Leaf Septoria, for example, is borne on the seeds the plants come from. Powdery Mildew is air borne as might Downy Mildew be.
Knowing which plant diseases affect which plants and the source of the pathogens that cause them would be of more help in the long run.

Here is a link that might be useful: About soil solarization

If you're attempting to render the soil useless, then useless is not a target specific approach :-) if you will... it's an all or nothing deal. Instead of trying to burn the soil, why not just dry it out if most of your problems are moisture content related and add some porosity to the soil by increasing the void space in it?