I've started this suggestion twice and abandoned it because I couldn't seem to describe it adequately without photos or illustrations. I hope this works.
Take your GFG "squares" and draw a pattern around the edges. Use newspaper or whatever to make the pattern with. Cut it out and then cut in 1/2. Then, "hollow" it out, leaving about and inch and a half around the edges. Now, you'll have to add a seam allowance to the edge. So, what you have at this point is a crescent shape that matches the edge of your "square". This will be your pattern for light fusible.
Given it's shape, you should be able to cut multiple crescents from a small amount of fusible. Sew two pieces together to form a circle. Sew this onto the front of your GFG "squares". Turn it and it's ready to fuse to your background fabric.
I bought a Dresden plate quilt kit at an estate sale last year. This is how I intend to give it a turned edge and hold it until I get it blanket stitched to the background.
If it doesn't make sense, let me know.
bkay