While I'm certainly not familiar with the construction of your rig: I did take a quick peek at mine own during lunchtime...
There definitely was enough trimwork around the slide, where a small D-ring could be hung. After all: the weight of the door is pretty small...
And no holes would have to be drilled in anything that is load-bearing. For that matter: you could even get a plastic one, and epoxy it in place.
It's just a thought...