Thanks for sharing. There are probably some options then. I know that Kies Air has had its ups/downs the past few months. I gave up on it due to some earlier instability that Kies Air had, but decided to check it out again just now as its free and comes with the stock OS. Kies Air does have the ability to browse the external SD card (screenshot attached).
I think AirDroid can do the same if I'm interpreting the difference between "System" and "SD Card" correctly. The File sharing feature (DLNA) would be nice if it worked. Thats under the Wireless and networks/Media share section in Settings. There are probably other good apps in Google Play that either function as a NAS or web server from which you can access files. Another thing I do is copy files to/from my S3 via FTP. I have a Mac Mini running FTP service on my local home network, and use AndFTP to move stuff around. From the shared storage that hangs off of the Mini, I can grab stuff and or place it on the common share for others to access. Works nicely as well.