The procedure I used to clean mine is described in post 136 of this thread:
https://www.airforums.com/forums/f51...-131783-6.html
My cleaning problem was a lot worse than yours so I think you'll have good results. I used Oil Eater and cold water. The pleats stayed firm and crisp, so if I were doing the cleaning again I would open the folds up--not worry about the pleats.
I did look into replacing the foldette doors and IIRC the price was $189 in 2016.
To update my story, the foldette doors cleaned up fine and we reinstalled the one between the galley and the bathroom/shower area. The other, which separated the bedroom from the bathroom/shower area, also cleaned up fine, but we have chosen not to reinstall it.
5 years later, so far so good.
Burnside