Nope, trying to hide it would probably just bring more attention to it.
If your door is built like I think it is, I would check with a fiberglass supply company and see if they can supply a new skin.
There are some pretty thin sheets of fiberglass, you may be able to reskin it without peeling the old sheet off. As long as your adding to the exterior and not chaning the hinge spacing it won't have any effect on the door operation.
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