Yes figured that out meanwhile, just a few minutes ago.
Basically using the same basic-install.sh script at /etc/.pihole is fine as the content is completely identical.
Important thing is: during running pihole -r, the script gets pulled again and therefore is the default version again. Luckily (for no reason as my OS is supported) running pihole -r for a 2nd time got stuck at the OS check level (I have the skip os check option set to true in my custom basic-install.sh).
Unfortunately, even running pihole -r did not solve my remaining issue (Conflict with other webservices running on Pi (Ports 80 and 443) - #73 by bcutter)
--> edit: web interface IP binding issue solved now 