On an invoice, how can I change the Expense Account that a billable expense is applied to?

Here is an invoice I have to pay for billable expenses.

There doesn't seem to be a way to select which account these items go against, enabling the expense account field it still doesn't provide the ability to edit.

I have also tried to replace the billable expenses with billable items, however this doesn't work either. Creating any item be it Other Item for Purchase, Service Charge for Purchase, Non-Inventory Item requires that I set a default expense account. Back on the bill, I am able to change the expense account for items and billable items as shown below.

But when I go to my profit and loss, the items are still showing up on the default expense accounts that are set on the item record.