On my Synology I run DSM 5.2 (the latest available for my model).
My open_basedir line is in /etc/php/conf.d/user-settings.ini
Maybe you can check if this file exists on your Synology?
On my Synology (DSM 5.2) the directory/file /usr/local/etc/php56/conf.d/user_settings.ini does not exist.
(Neither does /usr/syno/....).
Perhaps there are more differences between DSM 5 and DSM 6 than expected? And is the cops-package you used set up for DSM 5 or DSM 6. That should not but might explain your difficulties with setting up a working version of cops. I never used the package(s), set up cops from source. that's probably why I never encountered your problems.
And if I change open_basedir I need a reboot (or restart of the Synology web server).
Well,

that you were able to solve the problem and cops on your Synology works now.