Well, if you really have to, you can go to Publish View, and there you can create additional folders by right-clicking in the window. (See attached.)
You could create various folders to put your product images in, perhaps sorting them into categories. Once you've created the folders, find the JPG assets in Publish View, and simply drag them into the various folders you've created. When you republish, all associated links to the files will be updated by NOF. You could use the 300-odd
A bit of a drag with, what was it, 6,000 files? But would get you out of this jam until you find better hosting. (See below
)