How did you get iTunes movies to work?
I keep getting this message: "An error occurred trying to play this item. Please enable DRM support in your browser then try again."
I am sorry. Not sure why, but when I read your first post, I assumed you were talking about non-DRM movies.
Re-reading it, It says "iTunes movies", so maybe I was just really tired and missed it.
You cannot play DRM movies, such as ones purchased using iTunes, on Plex. There are some other options though (movies anywhere for example), but none of them will be fully offline options.
The closes offline option would be iTunes. You can move all your iTunes movies on an external drive (having a back up of these movies is a good idea anyways, so save them multiple places) and change your settings in iTunes showing where your files are stored.
This is not a fully offline option though, and only works temporarily offline, as the iTunes server will want to authenticate your account.
BTW, I use Plex for my massive DVD and Blu-ray library, and I used to use iTunes for it until I found Plex. I also own about 100 movies that I purchased via iTunes, but I don't ever watch them and have since replaced most of them with a DVD or Blu-ray, and they are now on my Plex library.