There's a good chance that your host doesn't like the fact that you're trying to extract a backup archive directly on the server – not because they're evil or something, but because they have strict restrictions on how fast you can submit requests from the same IP address.
There's a simple way to test that: extract the backup archive locally with Akeeba eXtract Wizard and upload all the files to your server. Then try to run the restoration.
If you still get an error the most likely culprit is the .htaccess file in the root of your main site. Please remember that .htaccess files cascade, i.e. a subdirectory of site inherits the directives from the .htaccess file in the root of the site. The best way to avoid this is to create a subdomain and place the subdomain root outside your main site's root (i.e. outside public_html, www, htdocs, http_docs or whatever your host calls it). Please consult with your host on the best way to do that.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!