3M also makes a headliner adhesive 3M 38808 which can take the heat much better and bonds better than 3M 77.
I'm sure there are also le$$ expen$ive headline adhesives at auto parts stores that should do the trick for door fabric.
E6000, for as many things it mentions about what it does resists, doesn't say anything about resisting HEAT as a headliner adhesive would need to resist. Especially being in the sun(roof of vehicle) and forces of gravity such as a headliner would be in.