What material did you use for the black fabric? I've had my door panels off plenty of times but I've never looked closely at those fabric-covered sections. Do those sections remove easily? I might get some fabric and try pulling/gluing it on myself.
I had a local boat upholsterer guy do it as I really didn't know what to use either. He used a sort of headliner material, it is a fabric not vinyl, but has a pretty soft texture. The guy told me it is pretty easy EXCEPT for the edge where it ends, he said it is very hard to make that look right. For mine he made a small welt around the edge, it looks really good in my opinion.
Those sections don't really "remove", what you have to do it peel the suede cover off and under that is a thin layer of foam that needs to be removed, much like the headliner. In my case it was worth it as I had put so much time into the headliner and wanted it to match and look good.
You can also use fabric paint, it looks really good but when it dries is has a rough texture, it is not very soft.