You may find that EL designs tend to be a little dense - try enlarging it a bit to see if that will help. They also have a Techniques and Tips section that addresses the many components of machine embroidery.
Cut-away stabilizer for heavy designs like this will work better than a tear away.
Cut away as much of the stabilizer as possible before pressing the finished design.
The cotton fabric you are using may be too light weight for the design selected. I have used undiluted liquid starch to stabilize the fabric for the block.
Cut the block larger than needed for the finished size.
Saturate blocks in starch and lay them flat on sweater rack to dry. I do this outside. If inside, lay newspapers under the rack to catch any excess starch that may drop from the fabric.
When almost dry, scrunch up and put inside a plastic bag for a couple of hours and it should be universally damp enough to iron smooth of any wrinkles.
I hope this works out for you.