I'm sorry, I don't like Annalyn.
I think it's nice that you are trying to honor all four grandmothers, but I think you are really going to limit your choices if you try to do so. Could you pick one grandmother from each side to honor?
I like Anna by itself, I also like Annabel.
If you really want to include all four, you could consider two middle names. For example, Anna Madeline Grace or something along those lines.