For a first quilt it is very nice. I haven't seen a butterfly hanky quilt before. I am by no means an expert but I have done quit a few appliqued quilts and I am not sure if it is possible to do what you are talking about. You will need to catch that bottom layer when you hand stitch that butterfly on in order for it to stay put. If you don't, I fear the new butterfly you add will become loose and floppy, so to speak. Having said that, you can do it with tiny stitches by hand and it won't look that bad, because the back is white already just use white thread.
Maybe someone else on here might have some other ideas for you, but in general a quilt requires to be quilted top and bottom, whether it has batting or not makes no difference because some summer quilts don't have batting, but in order for it to be firmly sewn together I would secure the bottom as well. When you go in, do add a small amount of batting to help hold it firm and not feel flat. I wish I could be of more help but you will do just fine I am sure.