I haven't appliqued a block that large. Looking at the picture, it appears to me that the background fabric has stretched primarily when the satin stitch was on the bias of the background fabric and/or around tight curves.
I have not had this problem when I have done satin stitch applique; however, instead of using stabilizer I heavily starch the background fabric. My method is to mix a 1:1 solution of Sta-Flo liquid laundry starch and water, "paint" this solution on to the background fabric yardage until the fabric is saturated, toss in dryer, and iron with steam before I ever cut the background blocks (and it's always a good idea to cut the background blocks a little larger, then cut down to exact size after the applique is finished). Spray starch will not be heavy enough, even if you apply it in layers. The 1:1 solution I use is the heaviest starch application I have found to be usable.
You might want to do some test samples before committing to another large block. Some types of fusible may not want to stick to heavily starched fabric. What brand of fusible are you using? I find most fusibles leave the hand of the fabric too stiff for my liking. I am just in the process of testing Misty Fuse to see how it works with starched backgrounds, and also to see how it holds up with different types of applique stitching around the edge. No results yet.
Are you sure you want to use a satin stitch? The satin stitch alone creates kind of a stiff, bumpy edge. A slightly more relaxed zigzag might work better if you don't mind the stray raw edge threads that will probably develop from multiple washings. Actually, a raw edge type of applique might actually enhance the monsters -- making them look more "monstery".