Hey, I think I solved this. Here is a better approach. In each of the modules (e.g. mod_CB_user.php) when they post a link to a profile using something like:
$url = "<a href='".sefRelToAbs("index.php?option=com_comprofiler&task=userProfile&user=$act_user")."'>";
Insert the function that retrieves the menu Itemid:
$url = "<a href='".sefRelToAbs("index.php?option=com_comprofiler&task=userProfile&".getCBprofileItemid()."&user=$act_user")."'>";
Using "unassigned" for the modules was not good enough because the menu navigation was messed up too. This fixes everything.