I don't know if you tried this yet, but we just collect the shells in a bowl or oven-safe dish near the sink (I use an 8x8 pyrex-type). Every other day or so, I pop the dish in a 350 degree oven for 10ish mins (usually when I'm cooking something anyway). It makes the shells easier to crush into tiny fragments, membrane and all. I use a potato masher -- my kids love to do this part. Seriously, if you haven't tried toasting the shells first, it is a game changer!
We used to mix them with the oyster shells, but my chickens seem to prefer the egg shells over the oyster shells, from what I've noticed at least. Now I just dump them in a little pile near their feed. We have had the same bag of oyster shell for ages, because the chickens are basically ignoring it and gobbling down the egg shells instead.
In the spring/summer, I often sprinkle the shell bits around the garden and flowers. I figure whatever the birds don't eat, either wild birds will eat or the plants will use as compost.