Izy, I use the freezer paper too..here is what I do differently-
I spritz it with spray starch and go ahead a pull my paper out before I sew it to the block. It stays turned under for me even without the paper in there.
I use invisible thread in the top and regular cotton thread in the bobbin and do the blanket stitch anyway. It is really hard to see it...looks almost like needle turned applique.
I even do it this way when sewing the appliqe by hand. I can't seem to master the needle turn as you go method..not enough practice I guess.
Have fun!