That is the default. All assets in root. Each page in its own folder (depending on the depth you have chosen).
You can create additional folders to hold the assets from publish view and move them out of root.
I talked to my datacenter engineers about the problem with your current hosting provider. They said I would not experience this issue as they use a dedicated backup system and dedicated backup storage unit for the daily backups. Their suggestion on your problem was the same as the one I originally gave you. Locate another hosting provider.
I do not think that you will ever be able to fit within the requirements that your hosting provider has set for you. no matter what you do, you are going to have a lot of files and you need to find a hosting provider who can accommodate you, not you bend and jump to their requirements.