Jottle

I'm posting here to get more traction outside of the tsx forum, but I'm hoping for some advice. I attempted (unsuccessfully) to load some furniture into the back of my '06 tsx, and in the process I pinched and puckered the black fabric on the top of the rear door. The car was sitting in the sun for awhile, so I think the glue holding the fabric in place was especially pliable when this happened. So now I have these puckered spots in the fabric that won't go away. I could just try and source a new door panel on ebay, but I was wondering if you all had any ideas for repairing this and getting the fabric back in place. I was thinking of leaving the car in the sun for a few hours again and attempting to massage the spots back down, but it looks like the fabric has been stretched so it won't be a perfect repair. A heat gun might give similar results. It seems like this isn't a piece of the door you can just replace. Any other thoughts?