the stiffness of a finished quilt is based upon the density of the quilting and the batting used.
just because you are doing free motion does not mean you have to quilt every space---batting like warm & natural you can have up to 10" between quilting lines- even the ones that need to be quilted every 2"=4" leave enough room for a nice, soft, drapable quilt.
if you don't like the stiffness- try a more (open) design. and perhaps a softer/loftier batt