Likewise, all of the garden beds in my raised garden had some tomato disease issues. I know it says (in the FAQ and elsewhere) not to compost diseased material. First, if there seems to be evidence that the disease is already everywhere in my soil I'm wondering if it is really a big issue composting it (wouldnt that be like "reinfecting" an already sick person?).

Second, I am wondering if I could burn or cook or heat treat (solarize in a bag?) any of these weeds or diseased tomato/cucumber plants well enough that it would be ok to add them to my (hot but imperfectly managed) compost pile. Its just an awful lot of material to be bagging and throwing out to a landfill if there is any other way.

FWIW, since many of these pathogens can remain viable in the soil from year to year, it is always recommended that you practice a proper crop rotation program to limit the infestations.

I leave seedy weeds in dark plastic bags until they are an anaerobic, stinky, slimy mess then put them in the compost. Seldom have plant diseases here but I expect they wouldn't survive such treatment. Of course there are things I can get away with in a cold climate that people in warmer ones can't. However in your zone 5 you must get some cold in the winter that might eradicate some plant diseases.