There are various theories why BER occurs, lack of calcium being the primary factor (often combined with excessive N). But inconsistent watering practices seem to play an equal role. BER often occurs when damper early season weather begins to dry out just as the fruit is beginning to set but can be just as frequent when the plants are allowed to dry too much in between waterings. I am not a big proponent of self watering containers and I am not familiar with your Garden Patch grow boxes to comment but I would do what I could to ensure the plants in them receive consistent, even moisture.

Bonide makes a calcium supplement for tomatoes called 'Rot-Stop' that is watered into the soil. I've never had to use it myself but it seems to be quite effective and is a popular item at my nursery.