what is the best way to repair vinyl sidelights to my home?

I have vinyl sidelights on the side of my exterior entry door to the house. I was scraping the paint to repaint them, and found that the pain stripper was making a mess....that's when I found out the sidelights were vinyl. I need to see how I can repair the textured mess that this has made. What products can be used to get back to a smooth coat so that it can be painted. What are my best options at this time, other than replacement. Any help would be greatly appreciated.