What is the stitch count on the EMB design? You are getting some pull in the stitching by looking at the pictures.
How are you hooping? Did you only hoop the stabilizer?
From a Floriani instructor "Hoop when you can hoop and fuse when you can fuse". If the design is over 8,000 stitches, add more stabilizer by floating a piece under the hoop. It can just be piece larger than the applique size and not a whole sheet.
I generally back all fabrics for applique ITH with a fusible product. Sometimes I even back the background fabric too. I don't use heat and bond for EMB applique projects ITH. I like a sheer cloth type.
Put the fused piece of fabric on the design slanted so it is not straight on. It helps prevents fraying when the design is trimmed.
Are you planning on quilting ITH too? I working on trying a new technique that I think will work. I just tried ITH quilting and like the finished results.
Are you adding stippling to the quilt blocks?
There is another product called no show mesh that can be used for EMB blocks. I leave it in the block. Just trim down around the basting stitch to avoid bulk in the seam lines. You can add the batting in square by square or as one full piece when making the quilt sandwich.
There are so many options for these projects and it takes time to discover ones that work. Here are a few tips.
https://www.emblibrary.com/EL/ELProj...ory=Fabrics101
PS: Most likely the blocks will look fine when quilted.