Welcome to The Quilting Board from Texas. I don't have any other suggestions for organizing your squares for your pillows but have seen some good ideas for you. If it were me, I think I would go with the zip lock plastic bags for storage & if you are afraid the bugs might eat through them you could then store the bags in plastic boxes.
I absolutely love your quilt gifted from your father during your college time. He could not have selected a better gift for you to cherish for your lifetime.
As I was reading your previous posts on the board about your pillow cases I have only one suggestion. If you are going to close them with a zipper you don't need a serger to finish off the raw edge along the inside of the zipper. You could use your zigzag stitch on your sewing machine & finish off the seam with the zigzag so the seam won't ravel.
Wishing you the best of luck with your new venture & thank you for your willingness to help your community learn new skills & allow them to earn more money for their families. This is a good thing you are doing.