I'm not entirely sure what the screenshots you put there are showing, but I can tell you how I did it 1 day ago and I will do it alike as soon as 1.0 is on the nitrado servers. managing the saves like that has been working without any issue for me.
- generate a [savename].zip in your client
- shut down the server
- save the existing [savename].zip you want to keep from nitrado servers to a place on your PC
- delete the [savename].zip existing on the nitrado server
- wait a bit (~2 mins)
- upload your new freshly (or already played) [savename].zip to the server
- wait a bit (~2 mins)
- boot up the server