Ok, I finally figured it out, and thought I share it here...
As I had the same template and quickstart version installed on another domain on the same server, I checked the settings and found as this install was on a sub-domain it inherited the PHP 7.1 settings from the main domain. Even though they were exactly the same than on the other domain with this quickstart installation, after setting the PHP 7.1 as dedicated to this sub-domain instead of the inherited ones, it started working... Not sure if that is a cPanel issue or just a strange coincidence, I thought it's worth testing for anyone who might encounter this.
Heiko