When you fed your cat Nature's Variety, did you gradually wean the cat off of the other food or did you switch immediately to Nature's Variety? Isn't it possible that the fruits and veggies increase the fiber content of the Nature's Variety to 3%. If you're feeding your cat a food with a much lower fiber content like Hound and Gatos, then the difference could cause softer stools at first.
Before I found Nature's Variety, I tried Weruva's Paw Lickin' Chicken which is a very good brand. My cat loved it but she would lick her hind leg until it was bald (probably a chicken allergy). She also became very constipated while I fed her Weruva and she would have pass a stool once every 5 to 7 days! It took me a while but I discovered the reason. One, the food was low in fiber and two, a large can of Weruva Paw Lickin' Chicken is only 84 calories. She had also lost a bit of weight while she was on it. Once I switched to Nature's Variety, she eventually had regular bowel movements again.