When I go into a task, and then 'edit this task', the list of projects in the ' Move this task (and its children), to project' section is not the full list of projects in the system.

Is there a reason for this, and is there a way to get it to show all projects?

Im pretty sure that only projects for the same company will show in the list.
try remarking line 218 in /modules/tasks/addedit.php, this wiil show all active projects in the dd menu