dollar store glue stick- just a small dab in the center of the piece- it holds for as long as you need it to- and disolves in water- so when removing your papers you can just spritz that first piece with water and it lets go. actually i just hold the piece or use a pin if i need to---but i was taught with the glue stick years ago. your problem with the fabric glue is---it's a permenent glue- you need a water soluble (cheap) glue.
have you tried water on the peice you can not get off? it might make it let go