I will jump in to provide my perspective but this may or may not help you.
Will your shared host not allow this?
private-folder/public_html
?
I know some of the most popular shared hosts allow this. To go one level below public. This is the ideal shared host set up:
private-flarum-files/public_html/public-files
Then you edit the paths in the appropriate files to point to the right directories.
You could try these instructions. See if something here helps:
https://discuss.flarum.org/d/25445-shared-hosting-installation-updated-2021