I've never done south beach, but I get my kids to eat veggies by getting the pured kind-think Gerbers for babies-and hide it in their food. It mixes well with sauces, in meats like meatload and burgers, etc. That might help you too. Or you can juice them. Same with eggs. You can make smoothies with the liquid pasterized ones so you won't taste it.
I hope it helps
Good luck!