Can buying MORE meat save me money?

I am slowly... ever so slowly... attempting an experiment in my grocery spending. I am trying to increase the meat/protein consumption of my family in an effort to feed them more nutritious food that will sustain them longer, thereby decreasing the AMOUNT and FREQUENCY of their eating.

Hypoglycemia is an issue with some of my family members, and this means that any type of sugar - even natural sugars - seems to increase their metabolism and they become hungry much more quickly. This means carbs are not necessarily a cost-effective way to keep them fed. Breads, pastas, muffins, etc. might be cheap for me to make, but in the long run, is it STILL cheaper? Not to mention, is it nutritious enough?

I got this idea from this post. I'll be sure to let you know how it's going.