I heavily starch my background fabrics for machine applique, and they don't require any additional stabilizer. This might work for embroidery also.
To do this I Sta-Flo liquid laundry starch 1:1 with water, "paint" this mixture onto the yardage until it is saturated, throw the yardage in the dryer, and then iron with steam before cutting. The fabric comes out about as stiff as a thin sheet of cardstock.
I have satin-stitched around small appliques with no problems, no tunneling, etc., and the starch washes out later.