When I try to install BoonEX 6.1.5, after it completes, it redirects me back to the installation

This issue is caused because the permissions suggested by dolphin at the end of the 6.1.5 installation are too restrictive for the 'inc' directories. To fix this, please set the following directory permissions -

755 inc/
755 ray/modules/global/inc

This will still provide you with the security that you need but provide usability.