Maybe Transmission wants the downloaded files to stay where they were downloaded, so that they are available as seeds for others using Transmission. That could be a reason that the script gets limited write access.
Another option might be that you start a script yourself and that script in turn runs Transmission. And when Tranmission has finished, the script moves the files to the external drive. (Did I get it right, that a script started by you can write to the external drive?)
Disadvantage: You need workspace for the files to be stored temporarily on the internal drive.