So far, these are the files I've had to change from 775 to 755 (but I don't know which files should be 644 vs 755, etc, so it's a crap shoot and who knows what security issues arise as unknowing user tinkers with file permissions to get a script to work).
oc-includes/osclass/install.php
oc-includes/osclass/install-location.php
oc-admin/index.php
And...the "modern" default theme bundled with osclass 2.3.7 (CSS styling) is also broken due to file permission settings, but I have no idea which files those might be. I either have to ask Hostgator why their servers are not "playing nice" with OSclass, or just wait for the devs to address this issue. Thanks for all the help!