I also bought some 3M spray adhesive and some headliner as it was the closest I could get to 3mm thickness. I cut the headliner out slightly smaller than the backing board and glued it on.
Then I cut the holes out for the window winder and door opener. I also removed as much of the original fluff and any old dried glue from the vinyl.
Glueing the vinyl back was tricky. The end result...not too bad for a hack. Not 100% perfect but good enough. Next time I need to use more adhesive as you can see.
One original interior door trim.
Thanks also to Stinky for the tips/tricks on how to do this.