I have also felt the need of have this feature and I have built an application to accomplish that work. The requisites for running it are having the mono execution environment installed and configuring transmission to expose its web server (at least for the localhost if the utility runs locally).
I use it daily in my environment (in fact it is installed on my crontab) and it is stable. In any case I will be glad to help with any issues you may encounter, just log them here:
Maybe, an even more flexible solution would be the option to run a script after seeding finished (like the script after download finished).
For moving the files by transmission, I see a problem - and that's the reason why I don't use the "incomplete folder" option:
I'm always groping torrents into multiple download folders - all under my "base" download folder. If transmission was supposed to use "downloading/seeding/finished" folders, it would need to check the torrent's folder against the corresponding "base" folder and create relative subfolders in the new status's "base" folder. I think that's not really easy to implement, especially if you have some exceptional torrents that are downloaded to a completely other location that's not under the "downloading base" folder. Where should it move these files to ?