Seeing the pink snail costumes floating around inspired me to finally write up the method I use for combining delicate fabrics with knits, because I wasted so many years fighting this exact battle. The short version: stop trying to sew them together as one seam and start treating organza as a trim you attach in stages.
First, stabilize everything. Cut your organza on the lengthwise grain and run a line of washable glue stick along the raw edge, then let it dry completley. Sounds fussy but it stops that horrible wavy distortion completely. For attaching it to a stretch bodysuit, I use a walking foot if the machine has one, otherwise a straight stitch with the tension dropped slightly and the fabric fed by hand. Never let the machine pull, let your hands do the work. The other thing nobody told me for years: attach organza edging to the fabric piece BEFORE you sew the garment seams. If you try to sandwich it into a finished seam, one of the two fabrics always shifts and the seam goes lumpy. When I started basting the organza flat first with a long stitch, then sewing the construction seam through everything, the difference was night and day.
Same trick works for sheer ruffles over glitter knits. Baste, then stitch, and walk away if it starts puckering, come back fresh.