I don't see why the sync would be impractical. It only needs to compare the Mac and Server directories once every hour, for example, and this generates very little traffic if nothing needs to be transferred. The beauty of this solution is that it can all happen automatically, so long as Yummy FTP is running. Ok, it won't be triggered automatically at the instant a new image is available, but it should suffice, even if it does nothing for a few days.
Remote zipping & unzipping is not yet implemented in Yummy FTP, that is correct. However this cannot be achieved via FTP - Yummy FTP will need to log into the server machine as if it were a normal user, via SSH for example, and then issue the required Terminal commands. So if you only have FTP access to your server, this feature will not be available to you.
There is no built-in functionality to delete server files after downloading them. I don't think any other FTP client offers this either. This sounds like a job for an AppleScript - sync every hour then delete all server files. This could be done with Yummy.