So I know your map will publish just fine as I was able to test publish it with no issue with the smaller files options set... The slow internet will cause issues because it does require that the client be able to connect to the gateway... and it must send a ping packet every once in awhile if its not able to do that it will disconnect you which will return back that error.
Catz so to work around the issue on your map. Go into the preferences and then goto document and there is two options for Optimizing saves select the Smaller Files one and your map will be publishable. If you do not select it your map will take up 12mb on Battle.net the reason for this is your custom loading image and its not compressed :P
So to clear this up... The editor adds a Other:Other variant by default. Also the default it creates is Other:Other. If your right click your variant you can set it as the default variant. Which means it will be selected when you host a game etc. You should provide a name for your variant as it just makes things easier.