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On some shared hosting, you can compress files using the cpanel. If you do that, then you can move a single file down and up to move your files, then uncompress the files on the target server. I've found that on some shared hosting servers, if you use a zip file for compression, file permissions may not be preserved. Using .tar compression seems to work, though. Just be sure you are in the same (relative) place in your directories where you compress and uncompress.

Thanks for the step-by-step!