I embroider my quilts all the time. I only use outline stitches on the 3 layer sandwich. If other embroidery designs are used, those with fill stitches they must be embroidered on the top only. Otherwise they'll be ugly on the back. The outline stitches look as good on the top as the bottom-at least they should!
Here's what I do:
Hoop the sandwich. Yes, it can be tricky but is worth the time saved quilting it on your own.
I use NO stablizer as the batting acts as the stabilizer, especially on outline, quilting designs. I only use a thin batting like Warm and Natural or a low loft fusible, batting.
I stitch out a sample first to test tension of the design. Often times I lower the top tension on my machine. I don't use the pig tail in the bobbin (for Berninas) and set up my machine for normal sewing. This evens out the tension.
I stitch out the design on my quilt and watch it carefully. I hold the fabric up lightly as the weight of the quilt pulls on the embroidery arm...especially if the quilt is large. I don't create any tension on the quilt I simply keep the quilt lifted up off the arm so it doesn't "pull".
Hope this helps. I embroider/quilt many of my quilts using my embroidery function. In fact, it's why I bought my machine to begin with. I don't have a long-arm, but this is the closest I can get to perfect feathers etc. I do FMQ a lot on my own, but the embroidery function makes it look so professional and perfect!