Very interesting situation
I believe star had some software for there other models to comunicate via the eithernet but I also believe they discontinued with this software when the 20R-III came out due to the fact that no one purchased the software after large investment costs on the other models.
I have seen several years ago some software that access the controller (18iTB) via the ethermet which was produced by Fanuc.
The only down side to this software is it gave access to every thing about the controller as it was used for R&D tool was its primary use.
The company only used it for upload/download programs and the software was expensive some 8 years ago.
As for the Fanuc EDM fanuc developed the whole package to work together as for the other machine tool buliders they would have to develope there own software to work together I believe.
It sounds like you are just about there with the task of loading software as I would not be surprised there is a parameter that is blocking you or that the machine tool bulder needs to change software to allow you access to the file icon as possibly been setup to block for virus protection.
I would ask Star again if there is some sort of protection and get the dealer to go back to japan for details.
It will be in the too hard basket for the engineers but be insistant and patient for a suitable outcome.
And if you get some results let me know