This quilt has already been done with beautiful close satin stitch, and won ribbons for it:
http://www.cherylquilts.com/affairs_of_the_heart.htm
And at 7in blocks, it's perfectly possible to do this, especially if you use a fusible, though some might not want that stiffness. Some of that could be avoided if the fusible is cut away in the centre of each piece.
I also think that if you did do satin stitch, you could probably do it all before the embroidery, because I have added my embroidery after all my applique, as far as I remember. (Memory isn't great, but even so, I doubt if there would be many places that it wouldn't work)
Re thread for embroidery I am using, it's DMC Stranded floss, and I'm using two strands, and a stem stitch, in shade 742.