OK, so I finally was able to reproduce your result.
Thanks for your detailled explanation, this means a lot!
With this added to gamemodes.txt:
and this added to gamemodes_server.txt:
and with the copied pictures in the 360p directory, I get it to work, see
https://i.imgur.com/v8hKL9D.jpg
The quite interesting and not understood part is, once I move the (empty) map definitions from the gamemodes.txt into the gamemodes_server.txt:
Then it no longer works, the preview pictures are gone, see
https://i.imgur.com/DZctb5d.jpg
So there is a difference between gamemodes.txt and gamemodes_server.txt.
I'm just not quite sure what to make with this piece of information now.