You might try ironing them on a piece of muslin then taking them off while still hot and throwing the muslin away. That should remove some of the sticky stuff and some of the stiffness. Try it on a piece you aren't planning on using to make sure it works for you. I've never tried it on Avery Fabric but I have on other things. You may still have to iron them onto some other fabric but a lot of the stiffness should be gone.