I may be out of line here, but there shouldn't be a need to remove hinges.
Cut a 1 inch wide strip of the covering that is a little longer than the elevator.
Crease that piece down the middle the entire length of it.
Place that piece in the slot between the elevator and the stab.
Tack it into place with your iron.
Bend the elevator down.
Now firmly iron the strip into place into the space between the elevator and stab.
You will have a little bump between the elevator and stab where the hinges are.
You can leave the bump or cut that area out......I leave the bump.
It is barely noticable.
Now your gap is sealed.
Iron the large sheet of covering over the stabalizer and over the elevator in one large sheet.
Do not try to iron the covering into the area between the elevator and the stab.
Now that it is ironed nice and smooth, take your exacto knife and carefully cut a slit down that slot between the elevator and stab.
Be careful to not cut into the 1 inch wide piece that you have ironed on to cover the gap and hinges.
Iron the covering into the slot.
It's really easy and you don't have to undo anything.
Think it out and give it a try.
You'll like it.