I have just done M/E on a nylon jacket for my neighbour. I was also very nervous of it going wrong. I used a fairly thick cutaway behind and used a light spray of adhesive (left to dry for 20 minutes) and it worked like a charm :) Good luck
Never done nylon but would suggest a heavier cut away behind.
I have used paper glue stick to hold odd fabrics in place onto the hooped tear away, allow to stand for a while it is safe and washes out. Tiny bull clips to peg to hoop sides have also worked for me.
My needle hates the sticky back stablizer it gets gunked up, so in between thread changes I rub a little baby oil on the needle and tissue it off.
Maybe a ballpoint needle so as to not cut through the nylon ???