Wrinkled door panel tops

[EL34]

The door panels on my 97 Legacy Outback have all wrinkled at the tops

I guess from being in the sun all these years.

 

The car interior is really nice and so I was thinking I would have a go at making the door panels look better than they do right now.

 

I was going to try and re-glue the top edges of the door panel material after stretching it tight again.

 

I pulled the worse door panel, took off the rubber weather strip and pulled back the top material a couple inches, just to where the door panel bends at the top.

 

No matter how hard I pull on the material the wrinkles don't come out.

Looks like the material has stretched and wrinkled itself into a permanent shape.

 

I left the panel out in the sun to get it warm and still no go.

 

I think I can make it look a bunch better than it did, but it will never be totally smooth.

 

Anyone else ever deal with this situation?

 

Here's a couple pics showing the problem.