Sounds like maybe your Thinfire paper is curling. Try cutting the paper to just 1/4-1/2 inch bigger than the glass. Papyros doesn’t seem to curl.
Or, maybe you aren’t using 2 layers of 3mm glass? Only one layer will pull in, dragging the paper with it. 2 layers will stay right there but round out the edges. 3+ layers will spread out.