I use the open weave drywall tape. I believe it's fiberglass threads.
I left the plastic over the hinge line but slit it at the hinge line. One needs to glue the tape to the foam itself, so I made a slit through the plastic, fore and aft about 1/2 in. from the hinge line and 1 1/2 in, apart, then peel back to plastic so the foam is exposed. Now, cut the tape about 1 by 1 1/2 in. and hotglue to the foam. While the hotglue is still melted, put the plastic back down over the tape, using a plastic card to push it down rather than the fingers.
I found that the glass fibres will loosen up too much with use, across the hinge line, so I put a thin strip of hotglue across the threads.
You might as well do this now.
On the elevator. I put the glass tape all the way across the hinge line, using the method above.