Potatoes

probably not a good idea as they are closely related and the fungal spores from the blight will be in the soil too.
not sure how/if you can 'clean' the soil.

No, is the short answere. The blight spores are still in the soil, as Seaburn says, and will affect your potatoes. I don't think that you can 'clean' the soil but will have to avoid planting potato family crops in it for the next for or five years - as in a rotation cycle.

The tomatoes had phytopthora infestines. Water the area with Bordeaux mixture and as said before, keep a strict rotation of crops.