I can confirm that MODx runs fine when running under the CGI / phpSuExec version (in fact I kind of prefer it now, since I never have to maintain file/folder permissions in association with it).
And it would also seem this free host might be using some kind of clustered server environment which may be affecting the include path. I assume in this clustered server environment, the include path is variable based on the server making the response, but if so, what is the proper way to get the path in this environment? I just put a site up on ValueWeb which does use a clustered environment, and had to add the following code in between the session_name() and session_start() calls in the StartCMSSession() function located in the manager/includes/config.inc.php file:
session_save_path('manager/sessions');
...as well as create the manager/sessions/ directory.
Not sure if this is really the problem in the case of this host, ’cause I don’t see any session warnings being issued, but it’s possible this is related to the issue and I wanted to mention it.