The problem is with the cost allocation when issuing the Direct Purchase invoice. You cannot allocate it to the cost of a specific project.
The only way to overcome this is to have a line item for each project on the service or items that you use to apply the cost to a dimension or project.
I understand that when you do an order or delivery, that it will not work, but there must be a way that these costs can be link to a dimension at some stage. Maybe when you pay the supplier, unless there is more than one dimension's items that you order from the same supplier.
One could then have different direct tax invoice, orders link to the specific project.