I love all the ideas above, and thanks for this post. We are gf/cf and always trying to find good new ideas for snacks.
DD LOVES the chicken liver pate recipie in NT. I used a mixture of olive oil and ghee in place of the butter and froze it in very small little containers and have pulled it out of the freezer here and there. Sometimes we eat it on Hol Grain brown rice crackers, but usually she just eats it with a spoon instead of yogurt.
Another huge hit for us has been a garbanzo bean recipie I adapted from Super Baby Food. You can use canned garbanzos, but I sprout mine and then cook them in the crock pot instead. Either way you do it, drain/rinse them and toss them with olive oil and spices to your taste. I love sea salt and rosemary, personally. Then spread out on a baking sheet and put in the oven at 400 or 450 to roast until brownish. You don't want to make them too crunchy; if you get it just right, the outside is crispy but the inside is smooth. And even overcooked and crispy, they are yummer. Dd can eat a cup of these in a sitting, she LOVES them. And seems to digest them pretty easily, don't know if that's an issue for you.
This is a little carby, but we can get sunflower seed butter from Once Again Nut Butters at the HFS and we really love that. I used a gf bread (and I recoginze that the bread and nut butter aren't NT friendly but they are at least natural and minimally processed) and cut out shapes with a cookie cutter. I have a heart, fish, flower, and duck, but I've also just used the top of a cup to do circles and knives to do squares and triangles. I spread with the seed butter and sometimes top with raw honey or homemade dried apricot or prune butter (again from Super Baby Food). It's a great snack or part of a lunch.
Will your kids eat olives? That's another big hit over here. Not so great for protein, but good for fats. Avacados are the same.
I also think that pieces of leftover meat make a great snack. Roast chicken, sausage patties from that morning's breakfast, chunks of roast beef. I cube them up and give them as snacks, alongside a piece of fruit usually.