Drupal has a few multisite configuration options, examples of which are here http://www.contractwebdevelopment.com/drupal-multisite-configurations-and-hosts - which would be the ‘best’ avenue to follow under a crazy domain insane hosting account?
Drupal multisite
I think the “cleanest” way to go is what the article at the link you provided refers to as “Multisite via symlinks” and, further, “Configuration with shell access”.
A really useful “graphical” representation of this approach can be found on usingdrupal.com. 
–rlparker