In my opinion you can go with restricting your viewer by adding a password on your main directory.
For that you'll have to click on the icon under security called as a password protect directories >>
click on public_html and fill up the required details.
In addition when ever you need to move the protection you just need to remove the password. One thing you can keep in mind, rename the directory something like “website is temporary unavailable ”.
The above scenario is just my recommendation.