I do machine embroidery on some of my quilts but not nearly as dense as you do. Almost all mine is just outline simple designs, redwork/bluework. I use either tearaway or cutaway stabilizer and leave about an inch of it around the design. I quilt with a Tin Lizzie and shadow quilt around the embroidery catching the stabilizer in the quilting. So far this has worked for me.
Welcome to the board and I hope you will post pictures of your projects,I'd love to see them!