Project Costing - Cross Charging

We have 5 Operating Units, all in their own Legal Entities.  We use primarily capital projects.   We need to be able to enter supplier invoices to projects in different operating units.  Does anyone have any recommendations on how to set this up?

I was thinking perhaps we could create a new organization to assign in the Project hierarchy and assign each OU as a subordinate to it, and make this the start organization in the project implementation options for each OU.  But I'm concerned about making this change and not being able to change it back if it doesn't work.

In the implementation options the cross charging setup seems to apply only to organizations within an Operating Unit or within a Legal Entity.  In our environment, each organization is it's own Operating Unit and Legal Entity - so we need to be able to charge across them.