I was quite successful regluing a complete headliner w/ a spray adhesive. The problem w/ hot glue is that the headliner will become saturated (fabric will absorb hot glue) and get stiff very fast. W/ spray adhesive the fabric will be pliable. You will be able to stretch and pull the fabric back to the edge. Heat is not an issue w/ spray adhesive. Use a brand name, 3M -45 General Adhesive is good. The spray can be messy, tape and mask the areas were over spray can occur. Fallow the directions on the can. Keep the windows open.
Buzz kill!
Great post--this is what I was going to suggest, also, Jinx. Let us know how it turns out, man.