WP Super Cache breaking Admin Toolbar in the Frontend

We recently shifted our WordPress installation from the rootfolder to it’s own subdirectory following the steps described here in an attempt to fix a 500 error that is occurring on our subdomain publisher.vegmomos.com (which does NOT run WP) apparently caused by the WP mod_rewrite rules located in the htaccess file. We could not fix the error though.

We then updated Worpdress to version 4.0 and as soon as we re-installed WP Super Cache the admin bar on the frontend displays broken as an unstyled list under the footer. We first checked the header.php and the footer.php to make sure wp_head and wp_footer are placed correctly as mentioned in other threads solutions. Now I am 100% sure there is something wrong with WP Super Cache. It worked fine before the migration and update, now I am not sure whether the problem is caused by the migration or the update.

Our site https://www.vegmomos.com is quite heavy and it is important for us to run WP Super Cache plugin to reduce the loading time, but we need the admin bar fixed.

Any suggestions what we could try to get the admin bar display correctly in the frontend?
Ps. any suggestions about the 500 error are also welcome.