Thanks to everyone that posted your answers in the comments. Here is what happened, and what should have happened:
As you may have guessed, like a good gringo, I went with option A.
I politely told the lady who was offering the food that I had already eaten and was full and satisfied. Thank you, but I am full and happy. And as reflected in the comments, this would have been a perfectly acceptable and polite way to respond had I been at a social gathering in the United States. The person offering the food would have happily moved on to the next guest to see if someone else would like to partake.
What should have happened:
Actually the B/C combo answer is probably the most correct.
Immediately after the woman offering the food had moved on to more willing recipients, the pastor we were sitting with (who had also previously eaten, but took another plate) informed us that culturally it was impolite for us not to take the plate of food specifically prepared with us in mind. Ouch. He explained that it is better to take the food and not actually eat it, than to decline it. You can pick at it a bit, save it for later, or just wait for an appropriate opportunity to dispose of it, but to not take it is bad. Very bad.
I like the share it with your kids idea too. This works as long as they didn't get their own first plate at the same time you did.
Lesson learned. (The hard way)
Since this incident we have asked several people to tell us more things like this that are social landmines waiting to be stepped on by some hapless gringos. What we have found though is that it is difficult to think of this type of thing before it happens. Try to think of some in American culture. It is not as easy as it would seem.
So when you are traveling in Latin America and someone offers you a second plate of food after you are stuffed to gills already, remember the Blackstocks and do the right thing.