Like 30-minutes mozzerella, the cheeses you mention are acidified with vinegar or lemon juice, the mozz with citric acid.
Cultured cheeses are acidified through the growth of the culture, so that they are a living entity, whereas the acid processed cheeses are heated up too much for them to still be living.
My experience with queso blanco and citric acid mozz are that they last about a week or less, then they start melting into a smelly, yucky mess.
It isn't the moisture content, it is the lack of life that destroys them.